Two-dimensional eight-level pulse amplitude modulation with trellis-coded modulation (2D-TCM-PAM8) is proposed to overcome the bandwidth limitation for high-speed signal transmission due to its high spectral efficiency. However, the high coding gain of the TCM can only be achieved in bandlimited additive white Gaussian noise (AWGN) channels and cannot be achieved in nonlinear channels without any equalizers. In the directly modulated laser and direct detection (DML-DD) transmission system, the transceiver nonlinearities and the interaction between DML chirp and fiber dispersion will introduce nonlinear distortion. To compensate for the nonlinear distortion, we propose a computationally efficient piecewise linear (PWL)-Volterra equalizer. In this equalizer, we first use the PWL to correct the skewed eye diagram and then employ a simple 2nd order Volterra to compensate for the residual nonlinear distortions. By using the PWL-Volterra equalizer prior to the Viterbi decoder, the high coding gain of TCM can be achieved. In the experiment, a 104 Gb/s 8-state 2D-TCM-PAM8 signal generated in a-20 GHz DML is successfully transmitted over 10 km standard single-mode fiber (SSMF) in C band, with the bit error ratio (BER) below the HD-FEC limit of 3.8-103. Compared to only using the conventional 2nd order Volterra equalizer with a similar BER performance, the PWL-Volterra equalizer shows 29% computational complexity reduction.