To solve this system of equations, we can add the two equations together:

A - B + A + B = 55 + 180
2A = 235
A = 235 / 2
A = 117.5

Now we can substitute the value of A back into one of the equations to solve for B:

117.5 + B = 180
B = 180 - 117.5
B = 62.5

Therefore, A = 117.5 and B = 62.5.