Can I backdate the opening of a ticket?

Only an administrator can do this.

You can only backdate the created date on a ticket once the ticket has been created. 

Once a ticket has been created then it can be edited.  Click on the edit button which will take you to the screen shot below.

Click on the "created at" tab which will bring up a calendar.  Select the date required and then submit at the base of the page.
 

The bar at the top of the page will show that the ticket was successfully updated.
 

clixifix will time and date stamp every time a user modifies the created at date.