Since you specifically state the question as it relates to E-AB, the reference to 91.319(f) doesn't apply. But 91.319(a) does apply.
From 91.319, the answer is "no".
§91.319 Aircraft having experimental certificates: Operating
(a) No person may operate an aircraft that has an experimental
(1) For other than the purpose for which the certificate was issued;
(2) Carrying persons or property for compensation or hire.
Your statement that "The aircraft will not be used for hire or compensation but to rent out to a pilot who wants to fly from point A to point B." is where you have erred. The FAA has interpreted that rental (or lease) of an aircraft with or without crew is a commercial operation that is "Carrying persons or property for compensation or hire."
So in the view of the FAA, renting the aircraft is a violation of §91.319 (a)(2).
You should also be aware that you could be violating access rules for your airport by operating a business that doesn't comply with the airport's minimum standards for business. That could get you kicked off the airport.
You also need to consider the conditions of any insurance policy that covers the aircraft.
That said, there's nothing that prohibits you (except possibly insurance) from loaning the aircraft to someone as long as you don't receive any compensation. Just be aware that the FAA interprets the term "Compensation" very broadly; e.g. excess fuel on return of the a/c could be considered compensation.
Final caveat: I'm not an aviation lawyer, so nothing I say should be considered legal advice. Contact the FAA, EAA (since this about E-AB) or an aviation lawyer if you want a more definitive answer.