Nine and twelve. 12 x 9 = 108, 12 + (-9) = 3
If you want a better answer, try to solve the equations a*b=108, a+b=3 by substitution. Simply plug in b=3-a for b in a*b=108 to get -a*a+3*a-108=0. Then note the discriminant is negative, showing there are no (real) solutions.
If you can use more than two numbers, try -3, -2, 2, 3, 3
-3 and -3
-21
19
77
-40
-3 and -3.
They are: 3+2 = 5 and 3^2 = 9
23
21
-1
7
-21