Visual Studio and Kentico on Server

While you can't open a solution remotely without remote desktoping into that computer, it is possible to configure the server to allow remote debugging, I know it exists but I haven't set it up myself.

https://msdn.microsoft.com/en-us/library/y7f5zaaa.aspx

Is the server on your network? If so, and you have access to it, you should just be able to open the solution by navigating to it. If not, and you want to modify it, you will have to copy the project to your machine.

You might want to look into using some source control and setting up deployments.