It is PROJECT template, not SOLUTION template, but you were close:
How to: Create Multi-Project Templates[
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In short:
To create a multi-project template
1. Create the projects to include in the multi-project template.
2. Create .vstemplate files for every project. For more information, see How to: Create Project Templates.
3. Create a root .vstemplate file that to contain the metadata for the multi-project template. For more information, see the first example in the following section.
4. Select the files and folders to include in your template, right-click the selection, click Send To, and then click Compressed (zipped) Folder. The files and folders are compressed into a .zip file.
5. Put the .zip template file in the Visual Studio project template directory. By default, this directory is \My Documents\Visual Studio Version\Templates\ProjectTemplates\
Good luck!