Remark
Let the larger angle = x
Let the smaller angle = y
If the angles are unequal but on the same side of the transversal, then they must be supplementary. That's where you get your second equation.
Equations
x + y = 180 Fact about angles and parallel lines.
x - y = 35 Given
Solution
Add the equations together
2x = 180 + 35 Combine
2x = 215 Divide by 2
2x/2 = 215/2 Divide
x = 107.5
The larger angle is 107.5
The smaller angle is 180 - 107.5 = 72.5
Question: Do they differ by 35?