From the condition, you have two equations


    y + x = 36    (1)    (total coins)

    y - x =  4    (2)    (four more dimes than nickels)


To solve the system, add the equations (both sides). The terms "x" and "-x" will cancel each other,

leaving you one equation for unknown y

    
    2y = 36 + 4 = 40,


from which you get


     y = 40/2 = 20.


So, there are 20 dimes.


Now substitute y= 20 into equation (1). You will get


    20 + x = 36,


hence


    x = 36 - 20 = 16.


ANSWER.  x = 16 (nickels)  and y = 20 (dimes).