It seems you want to rent a car in "Western" Europe and drive to Estonia, rather than fly there and rent when you get there.

Every mainstream rental company I have encountered will not let their cars go into Eastern Europe. When I rent in Berlin, for example, I am always cautioned "no driving into Poland", which is only about 70 miles away. It's an insurance matter - the experience being that cars going there often do not come back. Sorry if you are from Eastern Europe but that is how it is. They would also be very difficult to recover if broken down.

Renting locally is a little more straightforward. Some of the rental companies there still do it the "old way", complete with driver. Your business contacts where you are going are probably the best source of information.