Answer: 
-8 (or) 5 and 5 (or) -8
Explanation:
Let one of the numbers = x 
Let other number = y 
As the sum of two numbers = -3 
x + y = -3 
x = -3-y
As the the result of multiplication = -40 
xy = -40
(-3-y)*y = -40 
-3y-y² = -40 
-y²-3y+40 = 0 
-(y²+3y-40) = 0
-(y+8)(y-5) = 0 
(-y-8)(y-5) = 0
-y-8 = 0 (or) y-5 = 0
-y = 8 (or) y = 5 
y = -8 (or) y = 5 
when y = -8 
x = -3-y 
x = -3-(-8) 
x = -3+8
x = 5 
when y = 5 
x = -3-y 
x = -3-5 
x = -8