According to this website, it is "equivalent to 100 percent of the incoming solar energy" but from this diagram, that statement appears to be false as the incoming solar energy is 342 while the back radiation is 324.

Could someone tell me how to do it? Or is it just not possible?

The "equivalent to 100 percent of the incoming solar energy" reference in NASA's website is a rough approximation and it is not a result of some conservation law that says the two amounts must be exactly equal. It only means "we have estimated that the atmosphere's back radiation is approximately equal to the incoming solar radiation" (and indeed $324\ \mathrm{Wm^{-2}}$ is approximately 100 percent of $342\ \mathrm{Wm^{-2}}$). Other similar estimations are suggesting slightly different amounts and percentages, but all are more or less quite close to each other for each radiation component. See for example the respective figure in Chapter 2 of 2013 IPCC Report: