I solved this in about 1 minute by just reading the startup script (in my case /etc/init.d/oracle-xe):
less /etc/init.d/oracle-xe
At almost the beginning of the file I found:
ORACLE_HOME=[PATH_TO_INSTALLATION_INCLUDING_VERSION_NUMBER]
This was the quickest solution for me because I knew where the script was located, and that it is used for starting/restarting the server.
Of course, this relies on that the version number actually corresponds to the actual server version, which it should for a correctly installed instance.