iOS app Distribution outside of App Store We have an iOS application that we are looking to possibly distribute to a client through Apple Developer Enterprise Program.

This app is not public, so releasing it on App Store will not work. 

Ultimately, we are looking to send an invitation to users through an email, or direct the users to a iOS hosting platform where they can download the app.

If possible, we are not willing to manage device ids. The client will have users outside the organization (contractors) to which they will need to distribute the app.

How can we do this?
Your question seems quite unclear as you seem to have given the answer together with the question.

The way to do this is to apply to the Apple Developer Enterprise Program. Using that account you can create an In-House Distribution Certificate that you can use to sign your app with in Xcode.

After you have signed your app, you'll need to create a manifest plist file. Host the app (.ipa) and the manifest (.plist) in a folder on a web server, and send the user's an invitation via email.

The user will then be able to download the app, trust the enterprise profile and eventually run the app.