4 + 2i*sqrt(5) and 4 - 2i*sqrt(5)
[where i is the square root of -1]
Given a+b=8, we have b=8-a.
Given ab = 36, we can substitute b=8-a to get a(8-a) = 36, or
a2 - 8a + 36 = 0
Using the quadratic formula gives the two possible answers, which accounts for the fact that a and b can be switched without affecting the problem.
736
56
46
24
The two numbers are... -36 and -36
36
57
-18 and -18
324
-20
The two numbers that satisfy the given conditions are 4 and 1. When you add 4 and 1, you get 5. When you multiply 4 and 1, you get 4. The two numbers are 4 and 1.
-36