The structure of the particle unbound nucleus Li-10 was investigated in a kinematically complete experiment using the Li-9(d,p)Li-10 reaction in inverse kinematics at an incident Li-9 energy of 20 MeV/nucleon. The experiment utilized the S800 Spectrograph at the National Superconducting Cyclotron Laboratory to measure the outgoing Li-9 from the breakup of Li-10 in coincidence with the recoiling protons from the (d,p) reaction which were measured using an array of silicon detectors. Based on the kinematics of the recoiling protons from the Li-9(d,p) reaction, we measured a lower limit of Delta=33.10+/-0.08 MeV (i.e., Delta>33.02 MeV) for the mass excess of Li-10 which is consistent with previous measurements. Through the complete reconstruction of the breakup kinematics, the structure of Li-10 associated with a ground state Li-9 core was distinguishable from structure associated with a Li-9 core in its first excited state. The observed ratio of Li-9(*) core events to the total number of Li-10 events that were detected in the experiment was 0.10+/-0.04 at forward center of mass angles (2.7degrees to 9.5degrees), and 0.24+/-0.03 at more backward center of mass angles (11degrees to 26degrees). The resulting Q-value spectra was best fit with either a single resonance located at Q=-2.58(11) MeV [corresponding to a neutron separation energy S-n=-0.35(11) MeV] or two resonances located at Q=-3.00(24) MeV [S-n=-0.77(24) MeV] and Q>-2.43 MeV (S-n>-0.2 MeV).