Let them be x and y

Two numbers have a sum of 11 

"Sum" means to stick a plus sign between them like this

  x + y

So we're told that sum is 11.  So you stick an equal sign after that
and then stick 11 after that.  So you have

 x + y = 11

>>...Two numbers have...a difference of 67...<<

"Difference" means to stick a minus sign between them like this

  x - y 

So we're told that difference is 67.  So you stick an equal sign after that
and then stick 67 after that.  So you have

 x - y = 67

So you put those together as a system of equations



Answer:  x=39, y=-28

When you add then, 39+(-28) that's 39-28 = 11

When you subtract them 38-(-28) that's 39+28=67.

Edwin