(A, B, C) is one of (7,1,6), (8,2,7), (9,3,8), (1,7,2), (2,8,3), (3,9,4)
We can simplify the equation by reducing the letters that appear on the same column with + and - and we get
B+B and C+C end up with the same digit (from the units column).
This means that B and C differ by 5.
Now we can blindly stab at it.
Let's assume B = 1.
We immediately get C = 6 and now have
The value that fits for A is 7.
So we have (A,B,C) = (7,1,6)
Let's move on to B = 2. We get C = 7.
We get A = 8.
So we have (A,B,C) = (8,2,7)
For B = 3 we get C = 8.
Following the same logic we get A = 9.
So we have (A,B,C) = (9,3,8)
For B = 4 we get C = 9 and we have
This gets us nowhere.
For B = 5 we get C = 0 so this is wrong.
For B = 6 we get C = 1.
A should be 0. Which does not work.
For B = 7 we get C = 2 and A = 1
For B = 8 we get C = 3 and A = 2
For B = 9 we get C = 4 and A = 3