Two negative integers are 8 units apart on the number line and have a product of 308. which equation could be used to determine extra small or negative integer?

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.