The difference between two numbers is 10. The difference between their sqaures is 800. What are their numbers?

Let x, y be the numbers.

x-y=10.

x^2-y^2 =800.

(x+y)(x-y)=800

x-y=800/(x+y) =800/10 =80.

solve two equations

x+y=80.

x-y=10.

By adding

2x=90.

x=90/2 =45.

y=80-x =80-45=35.

The two mumbers are 45.35.