One number is 28 larger than the other their sum is 420 what are the two numbers?

There is a very simple way of solving this type of problem:

Call the sum S and the difference D, then the two numbers A and B, are:

A = (S - D)/2 and B = A + D

In this case S = 420 and D = 28 so (S - D)/2 = 392/2 ie A = 196 and B is 196 + 28 ie 224