That sounds interesting: it seems like they did EM to estimate the coefficients of an infinite-term polynomial (hmm, it couldn't *really* have been infinite, so either the polynomial converged or they just took many millions of terms). Once they believed they had modeled the rate of bug-discovery as a function of time they just solved the equation for bug-discovery = 0. As you imply, actually finding the roots of a polynomial that large would be too challenging, so they just scanned forward in time until they found the first (+ve) root.
Just guessing, but that seems a reasonable approach to do what you're describing. Does that sound about right?