We select a sample of low-redshift (z ~ 0.1) E+A galaxies from the 2dF Galaxy Redshift Survey (2dFGRS). The spectra of these objects are defined by strong hydrogen Balmer absorption lines (H-delta, H-gamma, H-beta) combined with a lack of [OII] 3727A emission, together implying a recently-truncated burst of star formation. The E+A spectrum is thus a signpost to galaxies in the process of evolution. We quantify the local environments, clustering properties and luminosity function of the E+A galaxies. We find that the environments are consistent with the ensemble of 2dFGRS galaxies: low-redshift E+A systems are located predominantly in the field, existing as isolated objects or in poor groups. However, the luminosity distribution of galaxies selected using three Balmer absorption lines H-delta-gamma-beta appears more typical of ellipticals. Indeed, morphologically these galaxies are preferentially spheroidal (E/S0) systems. In a small but significant number we find evidence for recent major mergers, such as tidal tails. We infer that major mergers are one important formation mechanism for E+A galaxies, as suggested by previous studies. At low redshift the merger probability is high in the field and low in clusters, thus these recently-formed spheroidal systems do not follow the usual morphology-density relation for ellipticals. Regarding the selection of E+A galaxies: we find that basing the Balmer-line criterion solely on H-delta absorption leads to a significant sub-population of disk systems with detectable H-alpha emission. In these objects the [OII] emission is presumably either obscured by dust or present with a low signal-to-noise ratio, whilst the (H-gamma, H-beta) absorption features are subject to emission-filling.