The answer is a = -4 and b = 0.
We can solve this by looking at a system of equations using what was given
a + b = -4
a - b = -4
Then add then two equations together.
2a = -8 ---> then divide by 2 for your a value
a = -4
You can then put that into the equation and solve for b.
-4 + b = -4 ---> add 4 to both sides
b = 0