No one can install these onto the 2014 Corolla because they have a huge design difference:
These headlights can only be installed on the 2011-2013 Corolla's only!
I found quite a few things:
GReddy e-Manage Programmable Piggy-Back ECU:
http://www.phantasmusa.com/greddy15500500.html
Power Enterprise Camcon Ti Cam Timing & Air/Fuel Controller:
http://www.fastscions.com/Scion-VVTi-Power-Enterprise-Camcon-Ex-Controller-CC-EXO.aspx
Unichip Performance Computer...
I remember reading on a different forum about some kind of part that would tune the ECU on the 10th gen Corolla so that it would let the full potential out of the aftermarket parts such as the exhaust. Once I find it, I'll update you guys on it.
My 2011 S almost had the same fate as your 2013 Corolla yesterday but fortunately, the damage from the accident wasn't as bad(luckily, the other person slammed the brakes) but it's getting repaired. Nice upgrade though!:thumbsup:
This picture shows the underbody covers on the car:
If you look at the rear wheels, you can see a highlighted part which could be the one the OP is talking about it.