The current ( i ) at time t = 0 and t = ∞ respectively for the...

At $t = 0$, current through inductor is zero,

hence ${R}_{eq} = \left(5 + 1\right) ‖ \left(5 + 4\right) = \dfrac{18}{5}$

${i}_{1} = \dfrac{E}{18 / 5} = \dfrac{5E}{18}$

At $t = \infty ,$ inductor becomes a simple wire and now the circuit will be as shown in figure

hence ${R}_{eq} = \left(5 ∥ 5\right) + \left(4 ∥ 1\right) = \dfrac{33}{10};$ ($∥ ⇒$ parallel)

${i}_{2} = \dfrac{E}{33 / 10} = \dfrac{10E}{33}$