Odd step in derivation of phasor Telegrapher's equations
Equations 2.17 are in time domain.  e^(jwt) is the representation of a sinusoid in the time domain.

Equations 2.18 are in the phasor domain.  In the phasor domain, the sinusoid is assumed - a phasor represents the amplitude and phase of a sinusoid, but a phasor is NOT a function of time and thus does not include a time domain represenation of a sinusoid.

I have borrowed from wikipedia below:  The equation in blue is the time domain representation - notice the dependence on both frequency (w) and time (t).  The red box shows the equivalent phasor form - notice that both frequency and time are missing.  A phasor is only valid at a single frequency, and that frequency is typically inferred from context.