let 'x' and 'y' be two numbers that have a sum of -10 and a difference of -2, then, we have the following system of equations:

notice that if we add both equations at the same time, we get:

now that we have that x = -6, we can find the value of y substituting x = -6 on any equation:

therefore, x = -6 and y = -4. Next, we have that the product is (-6)(-4) = 24