Two numbers differ by 7, and the sum of their squares is 29. Find the numbers.

let numbers are x and y. then x-y=7...............(1) and $$ x^2+y^2=29 $$ From (1), $$ \left(x-y\right)^2=49 $$ $$ x^2+y^2-2xy=49 $$ 29-2xy=49 xy=-10 then y=-10/x, Now from (1), $$ x+\frac{10}{x}=7 $$$$ x^2-7x+10=0 $$ so x=2,5, then y=-5,-2 So the numbers are 2,-5 or 5,-2