The secure sharing of data is crucial for peer-to-peer energy trading. However, the vulnerability of Information and Communication Technology (ICT) infrastructures to cyberattacks, e.g., Denial of Service (DoS) attacks, poses a significant challenge. A possible solution is to use Digital Twin (DT) modeling of the physical system, which provides robust digital mapping and Big Data processing capabilities that facilitate data recovery. To this end, this paper proposes a DT-enabled energy trading framework for cyber-physical energy systems that offers data analytic and recovery capabilities to defend from DoS attacks. With this framework, a new distributed approximate-newton trading algorithm with a switched triggering control strategy is proposed. Therein, the DT model is employed to achieve data recovery and adjust the system evolution of trading trajectory during attack periods. This enables the proposed method to find optimal trading solutions even in the presence of DoS attacks. Theoretical analysis results demonstrate the correctness of the proposed method. Furthermore, numerical simulations are conducted to assess the effectiveness of the proposed method.