Answer:
Both solutions fit the description. Either the numbers are -5 and -13, or they are 5 and 13.
Step-by-step: Numbers m and n.
Differ by 8: n-m=8
Product is 65: m n=65
Find m and n.
The Differ equation gives n=m+8. Use this in the Product equation.
m(m+8)=65
m^2+8m-65=0, which we can factor, so let's do that:
(m+5)(m-13) ---- will that work? No. Gives -8m instead of +8m.
(m-5)(m+13) ---- Will that work? Yes. 13m-5m=8m, and product in const. term is -65.
OKAY, solution to the quadratic formed is m=5 or m=-13.
What about n?
n-m=8
n=m+8
For m=5, n=13.
For m=-13, n=-5.
