Phase difference between resistor and inductor voltage in an RL AC circuit
The negative sign in the equation \$E = -L\frac{di}{dt}\$ implies back emf i.e. the voltage induced in the coil due to current flowing. Given that you might want to calculate the current that flows in an inductor for an applied voltage, the formula is \$V = L\frac{di}{dt}\$.

Note that I used the voltage symbol "E" for back emf and "V" for applied voltage but please get used to them being called "V" for both occasions and recognizing that the negative sign implies back (or induced) voltage (or emf).