Question 579381
Let X be the larger number
    Y be the smaller number

so The sum of two numbers is 48
 Can be represented as 

X+Y=48

and 

the difference of two numbers is 22

as:

X-Y=22

the, equate the two equation and add.

X+Y=48
X-Y=22     Y is canceled because they have diff. sign
------
  2X=70  
   X=70/2
   X=35
Substitute X to any of two equation.  
Let's use

X+Y=48
35+Y=48
   Y=48-35
   Y=13


Thus, the two numbers are 35 and 13