Depending what AirPort Express model you have, it is either possible or not.
If you have the first generation (2008 - 2012), then it is not possible, since it only has one Ethernet port. The 2012 model has two Ethernet ports (one for the connection from the modem to the AirPort Express and one for an additional device with Ethernet, like a switch or router.
Anyway, it is probably best to get a switch, if you have the 2012 (current) model. If not, it will probably be more tricker and a router needs to get involved.