How to balance reading the literature and just solving the problem your self?
There is a wonderful quotation by Frank Westheimer that accurately summarizes the relationship between work and reading:


  A couple of months in the laboratory can frequently save a couple of hours in the library.


If you don't know what's in the literature, you can easily spend days, weeks, or even months reinventing the wheel. It's tempting to get your hands dirty, but it can be a very expensive proposition if you later find that somebody else has already done the same thing.