How to solve equations where numbers are replaced by letters?

Question

Mathematics

Tell me, maybe there is a service or algorithm that could be used to solve equations of the form ABD + CD = AAD, where each letter is replaced by some number. The challenge is to find these numbers.
UPD: You need to solve in different number systems. Not only at 10.

Answer 1

can be solved analytically. For example, the example shows that D + D \u003d D, therefore it is 0. B + C \u003d A, Since the Number of the first digit has not changed, therefore B + C is any 2 numbers in the sum greater than 2 and less than or equal to 9.

Answer 2

Yes, just a bust, there are not so many numbers.