Answer
16 and 16.
Work Step by Step
Step 1. Assume one number is $x$, then the other number should be $32-x$
Step 2. The product is $P=x(32-x)=-x^2+32x$
Step 3. The maximum of $P$ happens when $x=-\frac{32}{2(-1)}=16$
Step 4. Thus the two numbers are $16, 16$ with $P=256$
