Ben
Favorite Answer
The rationality isn't really needed:
(x-y)^2 = x^2 + y^2 -2xy
= x^2 + 2xy + y^2 - 4xy
= (x+y)^2 - 4xy
= (6049/330)^2 - 4*84
so |x-y| = sqrt((6049/330)^2 - 4*84) = 1/330.
[Which, together with the sum, readily gives 3025/330=55/6 and 3024/330=504/55 as the two numbers.]