The sum of two numbers is 52. if twice the smaller number is subtracted from the larger number, the result is 13. find the two numbers.

To solve this equation, you know you have two numbers which you can represent with x and y. 
Larger number = y         Twice the smaller number subtracted from the larger
Smaller number = x       is equal to 13:

y - 2x = 13      Solve for y:    y = 2x + 13      Then substitute your value for y into the equation they gave you at the beginning:

(2x + 13) + x = 52    Solve the equation by simplifying:
3x = 52 - 13       3x = 39    x = 13           Then substitute your value for x (13) into the equation we made to solve for y:
y - 2(13) = 13      y - 26 = 13     y = 39     
So your answer is, "The two numbers are 13 and 39."