Radiant energy is essentially radiant flux integrated over time, since radiant flux is the amount of joules produced per unit of second (watts). Is this correct?
The difference between radiant energy and radiant flux is that radiant flux is per unit time (J/s). These terms are the basis of other radiometry and photometry terms that appear on the chart of terms on a later slide.
Both of you are right! It goes both ways. Since radiant flux is radiant energy differentiated w.r.t time, so if you integrate radiant flux w.r.t time, you lose the dt term and get radiant energy as a result.