Since t>w by adding a constant number s to both sides:

t+s>w+s but because we add the same number to both t and w it is unimportant in determining how much greater the sum of s and t is than the sum of s and w. (basically subtract s from the equation to get the original t>w.)

To find how much greater t is than w, take the difference.

t-w represents the 'some number' that is the difference between the two or the amount that t is greater than w by.

Therefore the sum of t+s is greater than the sum of w+s by an amount equal to t-w