With the increasing popularization of radio frequency identification (RFID) technology in the retail and logistics industry, RFID privacy concern has attracted much attention, because a tag responds to queries from readers no matter they are authorized or not. An effective solution is to use a commercially available blocker tag that behaves as if a set of tags with known blocking IDs are present. However, the use of blocker tags makes the classical RFID estimation problem much more challenging, as some genuine tag IDs are covered by the blocker tag and some are not. In this paper, we propose RFID estimation scheme with blocker tags (REB), the first RFID estimation scheme with the presence of blocker tags. REB uses the framed slotted Aloha protocol specified in the EPC C1G2 standard. For each round of the Aloha protocol, REB first executes the protocol on the genuine tags and the blocker tag, and then virtually executes the protocol on the known blocking IDs using the same Aloha protocol parameters. REB conducts statistical inference from the two sets of responses and estimates the number of genuine tags. Rigorous theoretical analysis of parameter settings is proposed to guarantee the required estimation accuracy, meanwhile minimizing the time cost and energy cost of REB. We also reveal a fundamental tradeoff between the time cost and energy cost of REB, which can be flexibly adjusted by the users according to the practical requirements. Extensive experimental results reveal that REB significantly outperforms the state-of-the-art identification protocols in terms of both time efficiency and energy efficiency.