Let's give it a try. Let the integers be x and y, understanding that both are -.
x - y = 8
x(y) = 308 Solve the first equation for x: x = 8+y. Subst. this result into the second equation:
(8+y)(y) = 308, or y^2 + 8y - 308 = 0
Quadratic equation with a=1, b=8 and c= -308.
-8 plus or minus sqrt(64-4(1)(-308) )
Then y = ----------------------------------------------------
2
Can you finish the arithmetic here? Find the 2 values of y.