Say I don't have a ideal transmission line i.e resistance/length!=0. Also E-Field exists between the two conductor lines. How then current flows through the line? There is no E-Field along the line right?
The following answer is related to RF communications transmission lines. In power transmission lines the answer would be a little different than the following.
Almost all RF transmission lines consists of two conductors. The purpose is to transmit a relative high frequency signal (electromagnetic wave) through the line by changing the voltage across the line following any AC waveform (mostly sine but triangular, square is possible). The change of voltage polarity from peak positive to zero and then to peak negative between the 2 conductors creates a permanent time changing electric field between these 2 conductors, which moves through the dielectric between them at a speed near the light speed (but never equal unless the dielectric is air). The speed is not of any concern since in our human perception it is "instantaneous". Then, what about the electric current? Since there is a change of voltage between the two conductors at any specific point, there must be also a change of the amount of charge that produce it. This change in electric charge at any point along the transmission line is produced by an electric current, back and forth, that exists because of the time changing voltage applied to the transmission line. So a back and forth electric current exist in a transmission line when an AC voltage is applied at any end of this line. Note that the transmitted information is received at the end of the transmission line by measuring the change in voltage at that end. By the way, a change in intensity and polarity of an electromagnetic field that hit a conductor also creates this change in current and, as a consequence, a change in voltage at the end of this conductor. This is the behavior of an receiver antenna.....
There is a voltage difference!
Say I don't have a ideal transmission line i.e resistance/length!=0.
Ok, a normal transmission line.
Also E-Field exists between the two conductor lines.
Ok, that's still the case with any normal transmission line. But why should it matter?
How then current flows through the line? There is no E-Field along the line right?
Why? Of course, there is an electric field along the line, and a current flows - as proven by usage of almost any hair-dryer or washing machine.
In fact, there wouldn't be an electric field along the line, if the transmission line was ideal.