Answer
The two numbers are -50 and 50.
Work Step by Step
Let the two numbers be $x$ and $x+100$. We want to minimize their product, the function:
$f(x)=x(x+100)=x^{2}+100x$.
$f'(x)=2x+100$, so our critical value is at $x=-50$. Therefore our two values are -50 and 50 ($x$ and $x+100$).