Windows Update Error Code 80072EE2 - How do I run windows update troubleshooter as privileged user

Nice catch, DSLev.
All Group Policy settings for Windows Update are contained under

HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Microsoft\Windows

Delete all Value Data for WindowsUpdate from the below subkey

HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Microsoft\Windows\WindowsUpdate

In fact, you can even delete the WindowsUpdate subkey as a system that updates directly from Microsoft's update servers uses these settings by Default -

HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\WindowsUpdate

And, as always, back up any key or subkey that you are going to edit in the registry first, just in case. ;)

80072EE2 is usually a temporary error connecting with the update servers that is caused by a Timeout, DSLev.

Is the system on a home network with a wired or wireless router ?
If it is, then suggest you plug it directly into the broadband router to see if the router is the cause of the Timeout error.

If a router is not causing the error, please try another attempt at updating. If/when it fails, close Windows Update.
Open the WindowsUpdate.log file and scroll down to the bottom for the most recent entries.
Copy and paste at least the last 50 or so lines into your reply, please -
How to read the Windowsupdate.log file

You can try resetting Windows Updates components by downloading and saving the Fixit on this page IF a router is not causing the Timeout error -
How do I reset the Windows Update settings?

When the download completes close all open programs and browsers. Then run MicrosoftFixit50202.msi and choose it's Default mode.
When the Fixit has finished running see if the system can update.

If it still can not, then run the Fixit again and choose it's Aggressive mode.
Restart when it's finished running and do a check for updates.