Will a Nikon 50 mm F/1.8 Lens work on a Nikon D50?

It's a Nikon series E lens. I purchased one online and I'm very afraid that it might not work on my Nikon D50 body? Will there be an adapter that I have to buy as well?

It will mount but won't meter nor autofocus. Sorry, there's no adapter.
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If you want an inexpensive 50mm prime, get the Nikkor 50mm/1.8D or G.

You bought a manual focus lens so you will have to use the electronic rangefinder in the D50 to focus.

How is it you bought the lens before making sure it would work on your dSLR? Isn't that sort of backward?

Here is a list of all the lenses made by Nikon and the cameras that support them

http://www.kenrockwell.com/nikon/compatibility-lens.htm

You may notice that NO "E" lenses are listed. They were only produced for a short period of time and AI-spec Nikon SLR bodies can use them.

As you will see, the AI spec lenses will work on your D50 but you will have to use an external light meter

In the future only buy Nikkor AF, AF-I or AF-S lenses for your D50

It will mount, it will work in full manual mode and without the benefit of a light meter. You're on your own with this lens.