Watch out, there are 10! = 3,628,800 combinations possible for a complete brute-force search.
There are some constraints to apply before you start, such as "leading zeros are not allowed", and "only a one is ever carried from the sum of two digits plus a possible carry" so:
B != 0
J != 0
A != 0
D + S = T or (T + 10)
I once implemented a solution for a peg-jumping game in perl by keeping a stack of game states, and doing all possible next jumps to make a stack of all possible next states, and so on. In your case a "move" would be the choice of another digit-to-letter assignment.
Test each partial solution for impossibilities and eliminate it from the list as soon as you can, so the problem does not grow exponentially.
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