Let the first number = x

Let the second number = y

According first condition i.e sum of two numbers is 42 ...we get

x+y = 42............(1)

According second condition i.e difference of two numbers is 30 ...we get

x-y = 30.............(2)

on adding (1)and (2)..we get...

x+y = 42

x-y = 30

--------

2x = 72 (+y and -y would be eliminated)

divide both side by 2 we get...

x = 72/2

x = 36

,,,to get the value of y, substitute the value of x either in (1) or in (2)...but here i took (1)....

x+y = 42............(1)

36 + y = 42

y = 42 - 36

y = 6

so the values are x = 36 and y = 6......

To verify your answer you can put the value of x and y in either (1) or(2)

or in both and you will always get LHS = RHS

please feel free to revert back for any further queries