set your first number to be x and your second number to be y;

therefore from the question;

x-y=12 ----(1)

xy=17 ----(2)

rearrange eq (2)

y=17/x ----(3)

and sub in to (1)

x-(17/x)=12

multiply by x

x^2 -12x - 17 =0

use the quadratic formula you get

x= 6 +/- SQRT(29)

then substitute both of those values of x back in to eq (3) and you get two values of y. Now check the corresponding values of x and y in the original two equations to see if both sets are solutions or only one set is a solution.