Magnetic reconnection is fundamental for the astrophysical and laboratory plasma. Its role is crucial in powering solar flares, production of energetic particles, and plasma heating. However, where the magnetic reconnections occur, how and where the released magnetic energy is transported, and how it is converted to other forms remain unclear. Here we report recurring bi-directional plasma outflows located within a large-scale plasma sheet observed in extreme ultraviolet and white light during the post-impulsive gradual phase of the X8.2 solar flare on 2017 September 10. Each pair of the bi-directional outflows originates in the plasma sheet from a discrete site, identified as the magnetic reconnection site. These reconnection sites reside at very low altitudes (< 180 Mm, or 0.26 solar radii) above the top of the flare arcade, which is only 4% of the total length of the plasma sheet that extends to at least 10 solar radii. Each arrival of sunward outflows at the looptop region appears to coincide with an impulsive microwave and X-ray burst dominated by a superhot source (10-20 MK) at the looptop, which is immediately followed by a nonthermal microwave burst located in the loop-leg region. We propose that the reconnection outflows transport the magnetic energy released at localized magnetic reconnection sites outward in the form of kinetic energy flux and/or electromagnetic Poynting flux. The sunward-directing energy flux induces particle acceleration and plasma heating in the post-flare arcades observed as the superhot and nonthermal flare emissions.