Firstly - it's good that you're OK and able to post! If you get *any* neck pain, get that checked out - whiplash can be nasty. Hopefully the other driver is OK as well (and any passengers involved in either car) - mistakes happen, I'm sure there was no malicious intent when the accident occurred.
On the car itself - primarily, bent chassis rails will total a car. Signs of that are doors that are not directly impacted by the crash appearing to "droop" or "sit up" because the chassis itself has bent and the doorframes are now mis-aligned with the chassis.
Otherwise, you're looking at a cost of repair vs cost of replacement calculation.
They're going to need to get the battery/etc out and check the boot/trunk floor underneath, it's likely crumpled (remembering that the boot/trunk is part of a crumple zone designed to absorb crash energy instead of transferring it into the "passenger safety cell").
It looks, at minimum, that you're going to need:
* rear bumper
* rear skirt
* two new mufflers (and confirmation that as they've deflected, they haven't bent the mid-pipes - if so, new mid-pipes as well)
* trunk lid repaired (minor scuffing visible in your shots on the bottom edge)
* A butt-load of clips/connectors/etc
As I said, I suspect the boot/trunk floor will be damaged and will require either panel beating or cutting out and replacing. The whole interior of the boot/trunk (and anything installed in that area - so battery, amp for the stereo, etc) will need to be inspected as well - in a crash, some items may have broken their mounts and come loose.
What I can't see in your shots is the right rear quarter panel - if it's suffered significant deflection, it'll possibly need replacement as well.
All rear suspension and drivetrain should be checked as well - if not for damage, then just for having moved from their stock positions/settings due to the force of the impact.
Get the car to a panel shop that you trust - if you don't know one, ask around (local car enthusiast forums/FB groups are a good place to start).
Best of luck with it! Hopefully if it is repaired they do a damned good job of it. I've had a car in the past damaged and repaired that was never the same after the crash, hopefully you avoid that circumstance!