Packaging always fails after installing Visual Studio?

Sorry, I meant is your project set up as a blueprint project or a C++ project.

Take a look at this answer: https://answers.unrealengine.com/questions/538760/error-windows-sdk-v81-must-be-installed-in-order-t.html

Just going off that first error message from the Unreal Build Tool, it would seem that you’re missing the software development kit. The link above suggests downloading it.

As Ninjin says - you probably missed a prompt during installation that would have installed this for you.