Wertheim's first order thermodynamic perturbation theory [M. S. Wertheim, J. Chem. Phys. 87, 7323 (1987)] has been extended to the two-dimensional tangent hard disk dimer for both the solid and the fluid phases. This extension utilizes pre-existing equations of state for the fluid [C. F. Tejero and J. A. Cuesta, Phys. Rev. E 47, 490 (1993)] and for the solid phases [B. J. Alder, W. G. Hoover, and D. A. Young, J. Chem. Phys. 49, 3688 (1968)], of the two-dimensional hard disk monomer system. The theory has been compared to simulation results and a good agreement has been found between them. Results are also presented for the fluid-solid tie line for m=2 up to m=30. The results of this work may be of interest to those involved in the study of chainlike systems adsorbed on a two-dimensional surface.