This seems to be extremely annoying. I create a blank solution and add an existing project or website to it and then the solution folder disappears and it just shows the added project, so I can't add any more projects or websites to the solution...
Update **
I'm not sure if this was from an extension or just by default, but in the Tools -> Options -> Projects and Solutions I found an option called "Always show solution" and it was unchecked. When I checked it the solution folder appeared so that I could right-click on it to add additional projects.
This may be because of the "Always Show Solution" setting that may be unchecked.
It can be found in the menu in Tools -> Options -> Projects and Solutions -> General.
When unchecked, it'll hide the solution item when there is one project (source).
Maybe you use VS express and there is restriction You can create just 1 project there.
To create a project and add it to a solution:
Read How to: Create Multi-Project Solutions for more information.
just open solution file > open solution .. then right click the solution folder > add project
Step by step
You need to set studio to always show the solution
From the menu: Tools -> Options -> Project and Solutions
Check the option: Always show solution
You can add an existing project simply going to File -> Add -> Existing Project....
This works and your solution will reappear in the Solution Explorer