The msi install packages are designed for silent installation - the installers of Test Studio can be downloaded in both exe and msi formats. These are available in your Telerik account under each of the products you are licensed for from the download section and you can give a try to the standard msiexec installer command line options.
I searched the web and also found an example of a Powershell script or using PsExec to install programs on remote machine.
However, you should know that these suggestions are not tested on our end as these are custom solutions, which depend on the specific environment. Still, I hope you will find the most appropriate for you,
Please, let me know if there is anything else we can be helpful with.