Question 1137225
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Let x = the ones digit and y = the tens digit.


You are given


    x - y = 2           (1)

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



Equation (2) is the same as


    (x-y)*(x+y) = 32.    (3)


In equation (3), replace the factor (x-y) by 2, based on the given (1). You will get

    2*(x+y) = 32,

    x + y = 16.           (4)



We are at the finish line now . . . 

Add equations (1) and (2). You will get


    2x = 16 + 2 = 18,


hence,  x = 18/2 = 9.


Then  y is 2 less than 9, i.e. 7.


<U>ANSWER</U>.  The two-digit number is 79.


<U>CHECK</U>.   9^2 - 7^2 = 81 - 49 = 32.    ! Correct !
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Solved.