Current of inductor in parallel to resistor
So how should I try to find the formula for the current of the
  inductor?


Convert the voltage source (E), R1 and R2 to a smaller voltage source in series with the parallel combination of R1 and R2. The new smaller voltage source value is: -

\$\dfrac{R2}{R1+R2}\$ multiplied by E (the value of the original voltage source).

Theory - you can convert "E" to a current source in parallel with R1. (see this page for Norton's theorum).

Once you have converted it, R1 is in parallel with R2 so now you back-convert to a voltage source in series with R1||R2.

You are now back to a single voltage source in series with a single resistor feeding an inductor.