  Excitonic insulator (EI) was proposed in 60's as a distinct insulating state
originating from pure electronic interaction, but its material realization has
been elusive with extremely few material candidates and with only limited
evidence such as anomalies in transport properties, band dispersions, or
optical transitions. We investigate the real-space electronic states of the low
temperature phase in Ta$_2$NiSe$_5$ with an atomic resolution to clearly
identify the quasiparticle energy gap together with the strong electron-hole
band renormalization using scanning tunneling microscopy (STM) and spectroscopy
(STS). These results are in good agreement with the EI transition scenario in
Ta$_2$NiSe$_5$. Our spatially-resolved STS data and theoretical calculations
reveal further the orbital inversion at band edges, which indicates the exciton
condensation close to the Bardeen-Cooper-Schrieffer regime.
