We have
xy = 14 ⇔ x = 14/y
x + y = 30 ⇔ 14/y + y = 30
⇔ 14 + y² = 30y
⇔ y² - 30y + 14 = 0
Δ = b² - 4ac = (-30)² - 4 × 1 × 14 = 844 > 0
y = (-b ± √Δ) / (2a) = (30 ± √844)/2
xy = 14 ⇔ x × (30 ± √844)/2 = 14
⇔ x = 28/(30 ± √844)
So we have x - y = 28/(30 ± √844) - (30 ± √844)/2