Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
There is no "upgrade", just "full" versions of 2016. So you simply uninstall 2010 and install 2016. The normal uninstall through "Programs and Features" will leave behind configuration files like normal.dotm and similar registry entries. When 2016 is installed, it will pick up on this information and use it.
This page has uninstall instructions if you need more details
Uninstall Office 365 / 2016 / 2013 / 2010 / 2007
https://support.office.com/en-us/article/Uninstall-Office-2013-or-Office-365-from-a-Windows-computer-9dd49b83-264a-477a-f8fcc-2fdf5dbf61d8?ui=en-US&rs=en-US&ad=US – ‘new” uninstall 365/2016/2013 page
Why do you want to "upgrade" to 2016? Do you NEED any of the new functions in 2013 or 2016? Or is that you simply have money to burn?