Find two numbers a and b whose sum a+b is -4 and whose difference a−b is -4.

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