You could say:
Written between 1/7/16 and 25/7/16
Started on 1/7/16; Completed on 25/7/16
However, normally the only date given is the date of completion and we don't bother with "Written by" or "On".
For example, the end of a report would simply look like this.
In light of the above, we will endeavour to complete the contract within the timescales agreed.
25th July 2014
Student or Learner