I've spent hours trying to figure this out. I hope what worked for me helps
someone else.
I tried all 8 resolutions from
www.updatexp,com/0x80072eee2.html
None of them worked.
I consulted the Windows Update troubleshooter that pops up when you "view
instatllation history" and click on the "failed" link. It suggested this
Open Internet Explorer
On the Tools menu, click Internet Options
click the connections tab, click LAN settings, and then click advanced
Delete any entry in the exceptions section
Close Internet Explorer.
Click Start, click Run, type cmd, and then click OK.
Type the following commands. Press ENTER after each.
net stop wuauserv
proxcycfg -d
proxycfg -u
net start wuauserv
This got me a new error: 8024401B.
A newsgroup post (thank you!) suggested this:
Go to Control Panel > Administrative Tools > Services and check if Windows
Installer is running. If not, turn it on. Doing this solved error 8024401B on
my computer.
Fixed mine, too! Thanks, rfshitop.