We demonstrate broadband wireless transmission at 2.54 Terahertz (THz) using directly modulated THz Quantum Cascade Laser (QCL) and Direct Current-biased optical orthogonal frequency-division multiplexing (DCO-OFDM). Fixed quadrature-amplitude modulation (QAM) transmission was investigated for modulation bandwidths of 2, 3, 4, 5 and 10 GHz, achieving gross data rates from 17.99 to 39.98 Gbit/s with modulation formats ranging from 16-QAM to 512-QAM. The measurements reveal a trade-off between modulation bandwidth, modulation order and bit-error rate arising from the limited usable bandwidth of the THz transmitter. Adaptive bit and power loading was subsequently implemented using measured subcarrier channel information, yielding gross data rates of 44.0 Gbit/s and 54.3 Gbit/s at the Hard-Decision Forward Error Correction (HD-FEC) and Soft-Decision Forward Error Correction (SD-FEC) thresholds, respectively. These results establish adaptive OFDM as an effective approach for efficiently utilizing the available bandwidth and increasing the throughput of THz wireless communication systems. To the best of the authors' knowledge, this represents the highest reported wireless transmission data rate at carrier frequencies above 1 THz.