This article explains why you can't install Microsoft Edge and run in Kiosk mode on Windows 10 LTSB and LTSC

Some customers wish to run their device in Kiosk mode using Microsoft's Edge browser. Elo devices that are sold with Windows 10 are LTSC versions and therefore may not have Edge and other apps that require regular updates, instead, these typically have Microsoft's Internet Explorer. This is how Microsoft designed LTSB and LTSC. Therefore, if you have an Elo device that is running earlier versions of Microsoft Windows 10 LTSB or LTSC, it is not possible to install Edge or the Microsoft store on those machines, Microsoft disallows it.

Here is an official note from Microsoft concerning this:
Kiosk configuration - Microsoft Edge has many improvements specifically targeted to Kiosks, however Edge is not available in the LTSC release of Windows 10. Internet Explorer is included in Windows 10 LTSC releases as its feature set is not changing, and it will continue to get security fixes for the life of a Windows 10 LTSC release. If you wish to take advantage of Kiosk capabilities in Edge, consider Kiosk mode with a semi-annual release channel. Read more HERE

If you need to run a browser in Kiosk mode, you can do so in IE11. Please see our Knowledge Article HERE