Since you are already running TDE it means that TQt, the toolkit TDE is
based on, is already installed. My original suggestion was that *if* you
had kgtk wrappers installed (e.g. as part of a metapackage) *it* could be
the cause of the problem.

In any case, you should prefer using the official packages of the latest release (https://mirror.ppa.trinitydesktop.org/trinity/archlinux/) rather than unofficial PKGBUILDS on AUR since they might be outdated.

I think we must first find out the cause of the problem. I remember using
a fairly recent version of Firefox on TDE/Slackware and TDE/Devuan with no
problems.

--
Philippe