Network – How do I reinstall a WiFi adapter / driver without an internet connection?

I just removed Ubuntu Desktop with Tasksel from my Ubuntu Desktop installation to free up space because I'm no longer using the desktop. During the process, however, my WiFi stopped working and the device is no longer displayed ifconfig or iwconfig.

When running lshw -C networkis displayed as UNCLAIMED, Realltek RTL8188EE.

When running a live Ubuntu desktop hard drive, the network device was identified and I can connect without any problems. However, I can't figure out how to fix it on my main installation.

This device no longer has Internet access, but I can transfer debs / files from another PC if necessary.

How would I restore the device and allow it to connect to the WiFi again?