Microsoft Edge is a "trusted" UI App and a core part of the Windows 10 Operating System; it can't be removed by conventional means, just like Internet Explorer could not be removed from previous versions of Windows by conventional means. There are a couple workarounds, however:
You can run PowerShell as an administrator and run the following command:
This will show you a list of all installed Apps and Core features for Windows 10. Scroll down until you find the one with the name Microsoft.MicrosoftEdge. Copy (you can use your mouse to highlight the full name and then press Ctrl + C to copy it) or write down the PackageFullName, which will change depending on the build of Windows 10 you are using. For the RTM version released in July, that is:
Get-AppxPackage Microsoft.MicrosoftEdge_20.10240.16384.0_neutral__8wekyb3d8bbwe | Remove-AppxPackage
Get-AppxPackage *edge* | Remove-AppxPackage
This should remove the app. Alternatively, you can navigate to the Windows Apps install location:
And right-click the Microsoft Edge folder,
Microsoft.MicrosoftEdge_8wekyb3d8bbwe, and select Properties, where you can set the folder and all its contents to Read-Only (make sure the checkbox shows a checkmark, not a square). This will prevent Windows from making changes to the folder.
Then, you can open the folder and rename the Microsoft Edge executables (
MicrosoftEdgeCP.exe) and/or delete them.