Let the two integers be A and B.
Product: AB = -120
Sum: A + B = -2
From the Sum eqution, A = -B - 2.
Substituting for A = -B - 2 into the Product equation,
(-B - 2)B = -120
-B^2 - 2B = -120
B^2 + 2B - 120 = 0
(B - 10)(B + 12) = 0
B = 10, or B = -12, giving A = -12 or A = 10
The two integers then are: 10 and -12