Unfortunately, the package @wolfman suggested is not compatible with the Raspberry Pi (based on the arm architecture - PC/Mac are i386, amd64)
Instead, consider compiling the driver, which hopefully will build against the armhf architecture, but there could be a chance this driver is not compatible.
Also on the page, there is a compressed package containing a driver for your chipset.
This driver package is an improved version of the driver package that the Maxxter company provided for a wireless dongle of theirs. The original driver only works in Xubuntu 12.04 and Linux Mint 13, but the improved version also works in Ubuntu 14.04 and Linux Mint 17.3.
Here is a quote from How-to-install.txt:
- Download the driver package Realtek-RTL8192EU-driver.tar.gz into the folder Downloads.
- First unpack it in the terminal, because it's a compressed folder with files. In the terminal (use copy/paste):
cd Downloads && tar xvzf ~/Downloads/Realtek*.tar.gz
- Now go to the uncompressed folder: in the terminal (use copy/paste):
cd install_folder
- Finally: the actual installation. In the terminal (use copy/paste):
sudo ./install.sh
- Plug the wireless dongle with the Realtek chipset into you computer: it should be functional now.