If one of the numbers is (x) and their sum is 10, the other must be (10-x). Thus the product (p) will be

p = x(10-x)

p = -x^2 + 10x

A plot of this is shown in the figure. As x gets larger from 0, the product will increase up to the point where x and 10-x are of equal value. That occurs at x=5. At that point, the product is 5*5=25.

p = x(10-x)

p = -x^2 + 10x

A plot of this is shown in the figure. As x gets larger from 0, the product will increase up to the point where x and 10-x are of equal value. That occurs at x=5. At that point, the product is 5*5=25.