You might encounter issues with the WLE because of compatibility. By default, the package is compatible with the following versions of Windows: 32- or 64-bit version of Windows 7, or 32- or 64-bit version of Windows 8, or Windows Server 2008 R2. As you can see, there is no Windows 10 version supported.
To install them, right click the installation package and choose Properties > Compatibility, then select Windows 8 from the list and tick the Run As Administrator.
Launch the package and continue with the installation procedure. The update will take place automatically, if the WLE remains installed after you upgrade to Windows 10.
Download: http://windows.microsoft.com/en-us/windows-live/essentials