Let 'x' and 'y' represent the numbers

x + y = 28

y = 28 - x

The product is:

x*y = x(28 - x) = -x^2 + 28x

We need to find the maximum of the parabolic function: f(x) = -x^2 + 28x

The quotient in front of x^2 is -1<0 follows the function has maximum equal to:

f max = c - b^2/4a, where a = -1, b = 28, c = 0

f max = 0 - 28^2/(2*(-1))

f max = 392

By solving -x^2 + 28x = 28 we find

x1 = 26.96

x2 = 1.04

........

........

The two numbers are 26.96 and 1.04.