The difference be

Let the two numbers be x and y.

According to question -

x - y = 14.....(1)

x² - y² = 448.....(2)

From equation (1), we get -

x = y + 14.....(3)

Substitute the value of x in equation (2), we get -

(y + 14)² - y² = 448

⇒ 28y + 196 = 448

⇒ 28y = 252

∴ y = 9

Substitute the value of y in equation (3), we get -

x = 23

Thus, the numbers are 23 and 9.