An older RDBMS version can be opened with a newer version, but an upgrade needs to be done.
If the source instance was completely shutdown, or backup files taken when it was offline, a startup nomount and create controlfile if needed then 'alter database open resetlogs migrate;' followed by the manual upgrade steps are the way to go.
Upgrade for 11g is a bit different than for 10g, there is the usual catalog upgrade, it shuts down the instance when it finishes. Then a couple rdbms/admin scripts to run, plus setting the instance timezone version. If the 10g instance was using v4 that isn't too difficult, a `select * from v$timezone_file` if that shows version 4 the whole upgrade isn't much harder than a 10g upgrade/migrate.