The TE72 was mostly sold in North America, where it was called "Corolla SR-5", and called Corolla also in Europe.
The TE71 range in Japan were all badged Corolla or Sprinter, and never Celica.
E means Corolla/Sprinter.
"T18 SE" was a badge made up by Toyota Australia, who are never to be trusted. They did it so as not to conflict with the KE55s they were still producing in the Melbourne plant.
Just playing games with you Sam