According to my textbook 简明汉语语法 the parts after the verb 写 are so called complements, they are strictly differentiated from adverbs.
both complements are called:
- complement of result 完
- complement of possibility 得完
I assume the meaning of 写完 is "to write (and it is completed)". However, i can not find out myself what the difference to 写得完 is?