Question 382761
Let p, q be two roots of a monic quadratic polynomial {{{x^2 + bx + c = 0}}} (without loss of generality assume the x^2 coefficient 1).

By Vieta's formulas, the sum of the roots is -b, and p + q = -b, so b = -10. Also, the product of the roots is c, i.e. pq = 22 --> c = 22. Therefore we have established our polynomial

{{{x^2 - 10x + 22 = 0}}} which we can find the roots p, q. By the quadratic formula,

p, q = {{{(10 +- sqrt(12))/2 = 5 +- sqrt(3)}}}

Therefore the two numbers are {{{5 + sqrt(3)}}} and {{{5 - sqrt(3)}}}.