It happened to me, recently, to work on multiple .NET Core solutions from various customers, but I was not able to open them. Or better: Visual Studio was able to open the solution, but it couldn't load any of the contained projects.

First it showed the following error message: "One or more projects in the solution were not loaded correctly. Please see the Output Window for details."
Error-Message

Then the Solution Explorer showed all .NET Core projects unloaded.
Visual-Studio-solution

The Output Window displayed the following message for each of the unloaded projects: "C:\xxx\MyProject.csproj : error : The project file cannot be opened by the project system, because it is missing some critical imports or the referenced SDK cannot be found. Detailed Information: Unable to locate the .NET Core SDK. Check that it is installed and that the version specified in global.json (if any) matches the installed version."
Error-Message-2

As the message says, the issues is that there must be a global.json file in the folder structure, that specifies a .NET Core SDK that is not installed on the local machine.
You can simply fix the issue updating the global.json file, or installing the required SDK.