The sum of two numbers is 47 and the difference is 25 . what are the numbers?

The numbers are:  36 and 11 .

Explanation:

Let us represent the TWO (2) numbers with the variables;
         "x" and "y" .

     x + y = 47 .

     y − x = 25.

Since:  " y − x = 25 " ;

Solve for "y" in terms of "x" ;

  y − x = 25  ;

Add "x" to each side of the equation:

   y − x + x  = 25 + x  ;

to get:

   y = 25 + x .

Now, since:

  x + y = 47 ;

Plug in "(25 + x)" as a substitution for "y"; to solve for "x" :

x + (25 + x) = 47  ;

x + 25 + x + 47 ;

2x + 25 = 47 ;

Subtract "25" from each side of the equation:

2x + 25 − 25 = 47 − 25 ;

2x  = 22  ;

Divide EACH SIDE of the equation by "2" ;
 to isolate "x" on one side of the equation; and to solve for "x" ; 
 
2x / 2 = 22 / 2 ;

    x = 11 ;

x + y = 47 ;

Plug in "11" for "x" into the equation ; to solve for "y" ;

11 + y = 47 ;

Subtract "11" from EACH SIDE of the equation;
  to isolate "y" on one side of the equation; and to solve for "y" ;

 11 + y − 11 =  47 − 11  ;

            y = 36 .

So:  x = 11 , y = 36 ;

 Let us check our work:

y − x = 25 ;

36 − 11 =? 25 ?  Yes!

x + y = 47 ;

36 + 11 =? 47 ? Yes!

The numbers are:  36 and 11 .