We present the first large-scale study of E+A galaxies that incorporates photometry in the ultraviolet (UV) wavelengths. E+A galaxies are 'post-starburst' systems, with strong Balmer absorption lines indicating significant recent star formation, but without [O ii] and Hα emission lines which are characteristic of ongoing star formation. The starburst that creates the E+A galaxy typically takes place within the last Gyr and creates a high fraction (20-60 per cent) of the stellar mass in the remnant over a short time-scale ( -20] exhibit implied SFRs of less than 50 M yr , their luminous counterparts [M(z) <-22] show SFRs greater than 300 and as high as 2000 M yr , suggesting that luminous and ultra-luminous infrared galaxies in the low-redshift Universe could be the progenitors of massive nearby E+A galaxies. We perform a comprehensive study of the characteristics of the quenching that truncates the starburst in E+A systems. We find that, for galaxies less massive than 10 M , the quenching efficiency decreases as the galaxy mass increases. However, for galaxies more massive than 10 M , this trend is reversed and the quenching efficiency increases with galaxy mass. Noting that the mass threshold at which this reversal occurs is in excellent agreement with the mass above which active galactic nuclei (AGN) become significantly more abundant in nearby galaxies, we use simple energetic arguments to show that the bimodal behaviour of the quenching efficiency is consistent with AGN and supernovae (SN) being the principal sources of negative feedback above and below M ∼ 10 M , respectively. The arguments assume that quenching occurs through the mechanical ejection or dispersal of the gas reservoir and that, in the high-mass regime (M > 10 M ), the Eddington ratios in this sample of galaxies scale as M , where 1 <γ <3. Finally, we use our E+A sample to estimate the time it takes for galaxies to migrate from the blue cloud to the red sequence. We find migration times between 1 and 5 Gyr, with a median value of 1.5 Gyr.