Hi Beau. II'm Greg, awarded MVP for eleven years, Volunteer Moderator, and Independent Advisor here to help you until this is resolved.
Can I see a screenshot of the entire error so I can see what you're seeing? Here's how to take one and attach using Attach Image button in reply box: http://windows.microsoft.com/en-us/windows-10/o...
There are fixes for known issues of Epic Games online services installer failing to install:
https://www.epicgames.com/help/en-US/epic-games...
https://www.epicgames.com/help/en-US/epic-games...
https://www.epicgames.com/help/en-US/epic-games...
https://www.epicgames.com/help/en-US/epic-games...
Right click task bar to open Task Manager. If necessary show More Details
On Details tab look for msiexec.exe, highlight to End Task.
Now try install or uninstall again.
If this doesn’t help you can try to Fix problems that block programs from being installed or removed: https://support.microsoft.com/en-us/help/17588/...
This can be symptomatic of corruption. I would go over this checklist to make sure the install is set up correctly, optimized for best performance, and any needed repairs get done: http://answers.microsoft.com/en-us/windows/wiki...
Start with Step 4 to turn off Startup freeloaders which can conflict and cause issues, then Step 7 to check for infection the most thorough way, then step 10 to check for damaged System Files, and also Step 16 to test a new Local Admin account. Then continue with the other steps to go over your install most thoroughly.
Feel free to ask back any questions, or report back results as you go.
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Linked tutorial is from a trusted Microsoft MVP