The {82B9BEC0-C9CC-4423-B54F-61E3C4AF53D8} = {82B9BEC0-C9CC-4423-B54F-61E3C4AF53D8} line indicates that the Test2008 project has a declared dependency (set up via the Project Dependencies dialog in VStudio) on the project with the unique identifier 82B9BEC0-C9CC-4423-B54F-61E3C4AF53D8. You should be able to find a project with that same identifier in the same .sln file.
As for why the odd syntax of the line, I have no insider knowledge of the .sln file format. However, based on observation of other ProjectSection extracts in .sln files, I would have to guess that the .sln parser used by Visual Studio historically assumed that the ProjectSection lines will be in a key = value format, with key uniqueness enforced within any given section. I would also guess that the folks who implemented the project dependency functionality decided that, rather than mucking with the parser, it would be simpler to use projectId = projectId for their section lines since the keys are meaningless to them, but they are guaranteed to be unique if only one dependency from project A to project B is otherwise enforced.