The sum of two numbers is 1000 and the difference between their squares is 256000. Find the numbers.
Let the numbers are $x$ and $y .$ One of them must be greater than or equal to the other. Let us assume that $x$ is greater than or equal to $y$.
The sum of the two numbers is 1000 . Thus, we have $x+y=1000$
The difference between the squares of the two numbers is 256000 . Thus, we have
So, we have two equations