Ed had 9 more marbles than Doug. Doug lost some of his marbles at the playground. Now Ed has 13 more marbles than doug. How many marbles did Doug lose?
Ed had 9 more marbles than Doug. 

That means that if we start with Doug's number of marbles, and add 9, we'll get Ed's number of marbles. So: 

Doug's number of marbles + 9 = Ed's number of marbles

Doug lost some of his marbles at the playground. 

That means that Doug's current number of marbles is less than it was before. So: 

Doug's current number of marbles < Doug's original number of marbles

Now Ed has 13 more marbles than Doug. 

That means that if we start with Doug's current number of marbles, and add 13, we'll get Ed's number of marbles. So: 

Doug's current number of marbles + 13 = Ed's number of marbles

We can solve this system of equations to find out how many marbles Doug had originally, and how many marbles Doug lost: 

Doug's number of marbles + 9 = Ed's number of marbles
Doug's current number of marbles + 13 = Ed's number of marbles

Doug's number of marbles + 9 = Doug's