Find a starting guess \(t_0\).
Iterate a few Newton Raphson steps: \[t_{n+1} = t_n - \frac{E(t_n)}{E'(t_n)}, \qquad n=0,1,\dots.\]
Until convergence \(|\Delta t| < TOL\) and \(|E(t)| < RTOL\).
