I'm not much good at these Snowdrops and I could be getting the wrong idea but if you put it like this
  BRIDGE
   CACHE
  HIDDEN  


Then N would have to be an even number and I don't think that the zero would be B,C,E,H.
 But I haven't got any further!!

Thanks veggie I'll try that! Someone else solved it in 10 mins so I'm missing something simple & obvious

Hang on- if it helps I know that A=1 D=4 E=5 N=0

Ok I think that zero is N,
1 is A,
2 is I,
3 is R,
4 is D,
5 is E,
6 is G,
7 is B,
8 is H and
9 is C.
But don't take my word for it as I could be wrong!

That's helpful otherwise there would be thousands of answers.

I can see that as BRIDGE has 6 numbers, CACHE 5, and HIDDEN 6 that H has to be 1 more than B.
I can also see than as the 4th number in BRIDGE & HIDDEN is a D, that the C in CACHE under the Ds has to be either a 0 (but can't be as N is 0) or a 9, so C must be 9.

And from that, it is relatively easy to show that Veggie is correct.

Veggie that adds up, how did you get those answers?!

El loro & veggie, I still don't get it but thank you!!!!!!!

OMG I need to lie down.  

With a pen, paper and a lot of swearing but I couldn't have done it without the numbers you supplied!
I'm not very logical when I solve puzzles but I wrote it out like I showed you then did it again but instead of putting numbers in I put dashes - like you do in hangman. I put in the numbers you had given me and went from there.

If E is 5 then E and E -my plus sign doesn't work on this laptop!! - is ten. Put the zero down and carry the one. So in the next column then you have G and H plus 1 equals E. E is 5 so those numbers must either add up to 5 or 15. therefore G plus H is either 4 or 14 . It can't be 4 as the zero and 1 are already taken and it can't be 2 plus 2 as G and H are different numbers so it must be 14. 
Are you with me so far - I'm not explaining it very well. El Loro is better I think at the logic

Following on from my first post where I said that C must be 9:
I in BRIDGE + A=1 in CACHE = D=4 in HIDDEN. As a 1 is carried over from the next number it means that I has to be 2.
Then as R in BRIDGE + C = 9 in CACHE, but no carry over from the next number means that R has to be 3.
The G in BRIDGE + H in CACHE + the 1 carried over from (E=5+E=5=10) last digit = 15 (can't be 5 as a 1 gets carried over). So G+H=14. Because of the other numbers already known, the only answer is that they must be 6 and 8. But we don't yet know which is which.
Bur we do know that B has to be 1 less than H, and as 5 is already used up by E, it means that B has to be 7, with H 8 and G 6.
And there you have it.

So if G plus H plus one is 15 then you will have to carry one under the D plus C column.
You said that D is 4 so the column that says D plus C plus one equals D now reads as 4 plus ? plus one equals 4 - or a number that ends in 4 so it can only be 4 or 14. it has to be 14 not 4 because of the carried one and the fact that zero has been assigned to N. So the question mark which is C must be 9.

Well done El Loro. Thanks for explaining that so much better than I could, I know how I got there but couldn't explain it easily

Veggie, I used to do Alphanumeric puzzles quite often in the past, so I remembered how to do this one.

I wrote it down on paper and did the maths like veggie said and it totally makes sense now! I'm still going through how el loro explained it, but I have to say that I never would have thought to have done it like that! I can't thank you enough for your help

You're welcome Snowdrop, did me good to exercise my brain for once!

E+E = N or N+10

If it's N, then G+H = E or E+10

If it's E, then D+C =D or D+10 (which it can't be, without C being 10)

So, if it's D, then C must be 0 (unlikely, as otherwise CACHE would begin with a zero)
and I+A = D, or D+10

If it's D, then R+C= I+10  If it's D+10, then R+C+1=I +10 (we know it's +10, because B and H can't be the same, so H= B+1)

If E+E=N+10

Then G+H+1=E or E+10 

If it's E, then D+C=D, or D+10. (Making C a zero, unlikely, or 10, impossible)

If it's E+10, then D+C+1=D, or D+10 (Can't be D, as C would have to be -1, so C+1 must be 10, making C a 9)

So far, we know that H=B+1 and C is most likely a 9.

Now we know that I+A+1 = D or D+10

If it's D. then R+C=I+10

 If it's D+10, then R+C+1=I+10, or R+C=I+9

As C=9, then R+C=I+10 can be written as R+9=I +10, or R = I+1
And R+C=I+9, would be R+9=I+9 (impossible, as R and I are different numbers)

So, we now know that R is 1 bigger than I
R=I+1 
H=B+1
C=9

E+E=N+10, so N is 0,2,4,6 (can't be 8, as that would make E a 9)

That would mean that E is either 5,6,7 or 8

Trying the first option (N=0) would make E=5

G+H+1=5+10=15, so G+H=14, so 8+6, or 6+8, making B a 5 or 7.
As E=5, then B would be a 7

So, if N=0, then E=5, B=7, H=8, G=6 and C=9

I+A+1=D, so D must be 4 and I and A must add up to 3, making them 1 and 2.

We know that R=I+1, and only the 3 is left, so I must be the 2 and R would be the 3.

So, the order could be N A I R D E G B H and C

And, as it works out, I'm not going to check for any other N values.

Blizzy you missed this post didn't you?

Impressive, all 3 of you! Mr summer was impressed too, it's been bugging him as much as it did me!

 No!!! 

Maybe.  

You're well clever Blizzie innit!!
I wouldn't have been able to do it without the solved ones that Snowdrops gave me. I worked on the assumption that none of the 3 'numbers' that were words would start with a zero - but that could have I suppose.

I did too.

I couldn't be bothered going down that route!