We report a search for electron antineutrinos at KamLAND with an 8.3−30.8 MeV energy range via the inverse beta decay. In 6.72 kton-yr of KamLAND data, we found 18 neutrino candidates and no significant excess over estimated backgrounds. From data interpretation, with the assumption of some supernova relic neutrino spectrum predictions, we give upper flux limits of 60−110 cm−2 s−1 (90% CL) in the analysis range and present a model-independent flux. These upper limits are the most stringent for 8−13 MeV region. We also improve on the upper probability limit of 8B solar neutrinos converting into antineutrinos via the Resonant Spin Flavor Precession with the neutrino magnetic moment. Besides, we could set limits on the annihilation cross-section for light dark matter pairs to neutrino pairs.