What you're asking here is easy/moderate to implement depending on one detail: whether the number can be set by the system or if the user should get the option to set the number (with a suggested default and preventing duplicates).
If you can rely on system to assign the numbers, record ID can be used just for that purpose. For that, you will need only to set new display callback for Title field in tasks (or modify existing, but then epesi won't be subject to upgrades without re-applying the change).
The data is in task_callback table, field Title, freeze=1. It points to CRM_TasksCommon::display_title method. Either edit that method and add $record['id'] to string returned there or change the value in DB and use a method from your own, custom module (recommended).
Mind you - you won't be able to search by this field this way, but you can still quickly jump to any tasks by the ID using the new jump-to feature you can see above and to the left of the record/browse table.
If you want users to have option to modify the number, it will be a bit harder. You will have to add new field and add rules to that field to make sure there are no duplicates. It's a little bit more trickier, for more details consult http://www.epesi.org/index.php?title=Epesi_tutorial
Please note that the mechanism in tickets is essentially what I suggested as first solution. It doesn't allow you to edit the number.
Hope this helps,