What is the difference between 写完 and 写得完 ?
写得完: possible to complete writing
  
  写完: complete writing


Beginners often learn 能+verb first, but in many cases, verb+得+complement sounds much more natural when they want to express can/be able to + verb.

I'm aware of some languages, e.g. Japanese and sometimes English, that don't always strictly distinguish these two kinds of expressions, but Chinese does. Always keep in mind that 写得完 is stative while 写完 is dynamic.