I'm going to get you started. The first thing I do with these problems is make a table of the known information. Take a moment to draw out a chart with the percentages and masses of each isotope. Since you don't know the mass of oxygen 16, let's give it the variable x.
Percentages can be represented as decimals, with 100% equalling 1. You might know this, but you just divide the number by 100 to change it. So let's change them to decimals for ease. Now, you know that all of the percents must add to 100%, or 1. Therefore, 1 minus the mass of oxygen 17 is useful information. 1-.00035= 0.99965. Therefore, 0.9965-x must equal the percentage of oxygen 18.
You can use this information to make an equation. Solving to find x will give you the percentage of oxygen 16, and then you get oxygen 18 by subtracting that number from 0.99965.
How do we make an equation? It should look like this. (average mass of element)= (mass of isotope 1)(percent of isotope 1)+(mass of isotope 2)(percent of isotope 2).. and so on.
See if you can come up with an equation, and I will check back to help if you need it.