Given that the absolute value of a = 5, the absolute value of B = 4, and the absolute value of a + B = a + B, find the value of a-b

Given that the absolute value of a = 5, the absolute value of B = 4, and the absolute value of a + B = a + B, find the value of a-b

A:
|A | = 5, a = - 5 or 5
|B | + 4, B = - 4 or 4
|a+b|=a+b>=0
So: a = 5, B = - 4 or 4
So:
a-b=5-(-4)=9
Or: A-B = 5-4 = 1
So: A-B = 9 or A-B = 1