Answer
10 and 10.
Work Step by Step
Step 1. Assume one number is $x$, then the other number should be $20-x$
Step 2. The product is $P=x(20-x)=-x^2+20x$
Step 3. The maximum of $P$ happens when $x=-\frac{20}{2(-1)}=10$
Step 4. Thus the two numbers are $10, 10$ with $P=100$
