Hi Dirk,
Would you mind trying the following steps, I had really good success with them:
1. Enable "Sideload apps" in the the developer settings ( Settings--->Update & Security--->For developers)
2. Within the folder that you extracted the Collector for ArcGIS install files, double-click and install the following files:
a. Microsoft.NET.Native.Framework.1.3_1.3.24201.0_x64
b. Microsoft.NET.Native.Runtime.1.4_1.4.24201.0_x64
c. Microsoft.VCLibs.120.00.Universal_12.0.30501.0_x64
d. Microsoft.VCLibs.140.00_14.0.25426.0_x64__8wekyb3d8bbwe
3. Once these files are installed, open "Windows PowerShell and navigate to the folder where the "Esri.CollectorforArcGIS_18.0.1.0_neutral_~_eytg3kh68c6a8" file is found and run the following command:
a. Add-AppxPackage -Path Esri.CollectorforArcGIS_18.0.1.0_neutral_~_eytg3kh68c6a8.appxbundle
4. After the app installs, you wont get a confirmation that it finished, but you can double-check in the start menu to make sure the app installed.
5. Make sure to go back to " Settings--->Update & Security--->For developers" and change the option back to "Windows Store apps"