Let
x---------------> smaller number
y----------------> larger number
we know that
y-x=108---------> y=108+x
product------------> x*y-------> x*(108+x)-----> 108x+x²
find the derivative and equals to zero
dx/dy=108+2x-------------> 108+2x=0---------> 2x=-108--------> x=-54
then
y=108+x-------> y=108-54-----> y=54
the answer is
smaller number is -54
larger number is 54
