If you think of directions, East and West are 180 degrees apart from each other. In other words, going West after traveling East is like turning around and walking back.
So Sheldon actually is 20 miles towards West of the original location from where he started. He droves 15 miles to the East and then drove 35 miles West from that location. This means out of his 35 miles drive to the west, 15 miles drive brings him back to his original location and then 20 miles (35-15 miles) is towards the west of his original location.
First, what is the question that you need answered? Presumably, since you wrote, "Sheldon drove 15 miles East and then drove 35 miles West," you want the difference between the two points.
To do this, subtract 15 from 35 which equals 20.
35 miles - 15 miles = 20 miles
Sheldon started at Point A and drove 15 miles East. He would then need to turn around and drive back the same way he came to drive West 35 miles. At the 15 mile mark heading West, he would be back at Point A. He would then need to drive 20 more miles to finish the 35 miles West.
"Sheldon drove 15 miles east and then 35 miles west".
Since there is no specific question to this problem. The answer can be suggested by the responder. It could be a writing prompt for a English composition class.
What was Sheldon trying to prove?
What are the facts?
Sheldon drove 15 miles east and then 35 miles west. He ended up 20 miles west of his starting point. Maybe he was following the sun. Maybe he was testing the odometer in his car. Or maybe, just maybe, he drove 15 miles to the east to see the sun rise and then 35 miles to the west to watch it move through the sky. It is a mystery with out a question is is an opportunity to create a story.
Sheldon then drove 20 miles to the east and home.