y^2 - 2xy - 16 = y^2 - 2xy + (x^2 - x^2) - 16

= (y^2 - 2xy + x^2) - x^2 - 16

= (y-x)^2 - x^2 - 16 = 0

Adding x^2+16 to both sides, you get:

(y-x)^2 = x^2 + 16

Taking the square root of both sides, you get:

y-x = +/- SQRT(x^2 + 16)

Adding x to both sides, you get:

y = x +/- SQRT(x^2+16)