When you try to start the Windows 10 update assistant on a Windows 10 Enterprise; the tool is stopping at the beginning during the check up of the operating system.

To upgrade to the Windows 10 build 1607 (also called anniversary update !), go to the MVLS web site (the Microsoft Volume Licensing web site) and download the latest Windows 10 enterprise version. Boot on the DVD or USB containing this new version and perform a UPGRADE.

Else

I found another solution that actually works for Windows 10 Enterprise without the need to have an account on MVLS to download the new ISO file. First of all make sure you have a backup of your DATA. Then follow these steps below:
1.Open regedit.exe and navigate to HKLM\Software\Microsoft\Windows NT\CurrentVersion
2.Change ProductName to Windows 10 Professional
3.Change EditionID to Professional
4.Navigate now to HKLM\Software\Wow6432Node\Microsoft\Wind­ows NT\CurrentVersion
5.Change ProductName to Windows 10 Professional
6.Change EditionID to Professional
7.Close regedit.exe (no need to restart)
8.Start the Windows 10 Pro installation from your installation media. (Download the Media Creation tool from Microsoft – http://go.microsoft.com/fwlink/?LinkId=691209 or https://www.microsoft.com/en-gb/software-download/windows10 and click on the Download Tool now)
9.Do the upgrade, will download and install, keep all files & settings.
10.Will reboot several times, once finished, log back in with your Microsoft Account and it will automatically link your enterprise key to the install and you will be back on Enterprise Edition and have Build 1607 installed.