You mean old database is 10G XE?
You need first backup old install, then remove old install, make new install and then restore.
There is no other way "upgrade" as I know.
Yes indeed, Jariola is correct as far as I'm aware, he (?) gets the answer points.
XE is intended as a "one host, one install" setup. One can not run multiple database instances with XE, also if other ORACLE_HOMEs are installed on the host that can lead to troubles. Best to install XE last for that scenario, and the older 10g (?) install has to be removed before the 11gR2 install can get started.
Although I've not tried it, it *might* be possible to completely shutdown the old (10g?) instance, make a backup of the controlfile(s) and datafiles, deinstall, install 11gR2 XE, shut it down, replace datafiles and controlfile with the old 10g flavour files and do the startup upgrade; steps- but that isn't an easy process for the novice.
An export (exp or datapump) of the 10g source before the deinstall and grabbing a copy of the dumpfile(s) and put them somewhere the deinstall won't touch them would be a less challenging way to go.