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(This problem can be done by guess and check. Below is the algebra way.)
Call the two numbers x and y. Then
xy = -9 and x + y = -8
Substituting x = -8 - y into the first equation:
(-8 - y)y = -9
-8y - y^2 = -9
y^2 + 8y - 9 = 0
(y + 9)(y - 1) = 0
Solving this equation gives y = 9 and y = -1, so the two numbers are -9 and 1.
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