Complex sentence: The second letter explains that Jekyll, having previously indulged in unstated vices (and with it the fear that discovery would lead to his losing his social position) found a way to transform himself and thereby indulge his vices without fear of detection.
Split into simpler sentences: The second letter explains that Jekyll had indulged in unstated vices and feared that discovery would lead to his losing his social position. He found a way to transform himself and thereby indulge his vices without fear of detection.