Question 862390
Let first number  = x
Let second = 2-x, as they add to two

{{{x^2+(2-x)^2=100}}}
Square 2-x
{{{x^2+x^2-4x+4=100}}}
Combine like terms
{{{2x^2-4x+4=100}}}
Divide both sides by 2
{{{x^2-2x+2=50}}}
Subtract 50 from both sides
{{{x^2-2x-48=0}}}
Use the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (2 +- sqrt( -2^2-4*1*-48 ))/(2*1) }}}
{{{x = (2 +- sqrt(4+192))/2 }}}
{{{x = (2 +- sqrt(196))/2}}}
{{{x=(2+14)/2}}}OR{{{x=(2-14)/2}}}
{{{x=8}}}OR{{{x=-6}}}
<h3>The numbers are 8 and -6</h3>