Lets name the two numbers x and y, so:
[tex]x-7=y[/tex]And
[tex]x\cdot y=294[/tex]Using the first in the second we have:
[tex]x(x-7)=294[/tex][tex]x^2+7x=294[/tex][tex]x^2+7x-294=0[/tex]Using the quadratic formula we get two values 14 and -21, the only one that satisfies both conditions is 14.
So the numbers are 14 and 21.
[tex]21-14=7[/tex][tex]21\cdot14=294[/tex]