When attempting to get the updates from Windows Update, error code 80072EFE occurred this time. It was resolved by applying the following three solutions:

Updating the Windows Update agent to the latest version.
http://download.windowsupdate.com/windowsupdate/redist/standalone/7.6.7600.320/windowsupdateagent-7.6-x64.exe

Enabling TLS 1.1 and TLS 1.2.
MicrosoftEasyFix51044.msi

How to fix errors 0x80096010, 0x800b010a, and 0x80092004 during installation of update programs.
KB3140245