Cross-section angular distributions of 38 (p, t) transitions to final states of Sn118 up to an excitation energy of 3.597 MeV have been measured in a high-resolution experiment at an incident proton energy of 21 MeV. A distorted-wave Born approximation (DWBA) analysis of the 38 experimental differential cross sections, carried out by using conventional Woods-Saxon potentials, allowed us either 18 confirmations of previous spin and parity values or new assignments of spin and parity to 14 states of Sn118. A shell-model calculation has been performed by using a realistic two-body effective interaction derived from the CD-Bonn nucleon-nucleon potential. The doubly-magic nucleus Sn132 is assumed as a closed core, with 14 valence neutron holes occupying the five levels of the 50-82 shell. Within this model space the calculations are performed by employing the seniority scheme including states with seniority up to 4. The energy spectrum of Sn118 has been calculated and compared with the experimental one. The theoretical two-neutron spectroscopic amplitudes are used in the microscopic DWBA calculations of some cross-section angular distributions.