The sum of two numbers is 24 and the sum of their squares is 386. One of the numbers is:

Explanation

Let the two numbers be x and y.

x+y=24

and

x^2+y^2=386.

Using

(x+y)^2=x^2+y^2+2xy,

576=386+2xy

xy=95.

So the numbers are roots of:

t^2-24t+95=0

(t-19)(t-5)=0.

Hence the numbers are 19 and 5, and 19 is the listed answer.