Question 819516
Let p = the product of the two numbers, x and y.
{{{y-x=11}}} and {{{xy=p}}}

{{{p=x*(x+11)=x^2+11x}}}
A parabola with a minimum.  Looking back at the factored form for p, roots are at x=0 and x=-11.
The minimum occurs exactly in the middle, for {{{highlight(x=-11&1/2)}}}; find also that {{{y=11+(-5&1/2)=highlight(5&1/2=y)}}}