If what you expect is the easiest way, then don't embed setup.exe as a resource, but as Content.
(Add setup.exe to your project, and right click on setup.exe in Solution Explorer to edit properties, set as content, and select Copy if newer.)
Another option if setup.exe is a project of your Visual Studio solution, is to automatically copy setup.exe in the output directory of the launcher project: Add a reference to setup.exe if it belongs to the solution, so it is automatically copied every time you compile and there was a change.
Last is the code that is pretty easy - you already have it, actually:
System.Diagnostics.Process.Start("HelloWorld.exe");
If needed, you can change the current directory:
Environment.CurrentDirectory = @"c:\someSetupExeDir";
But better, you can use Path.Combine:
String fullPath = Path.Combine(directoryPath, fileName);