Explanation:

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

Difference between their squares is 

equal to 448

x^2 - y^2 = 448

( x + y ) ( x - y ) = 448

( x + y ) × 14 = 448 

[ from ( 1 ) ]

x + y = 448/ 14

x + y = 32 ----( 2 )

Add equations ( 1 ) and ( 2 ) , we get 

2x = 46

x = 46/2 = 23

Put x = 23 in equation ( 2 )

23 + y = 32

y = 32 - 23 = 9

Required two numbers are x = 23 and y = 9

Hence, option 3 is the correct answer.