How is it possible to have high voltage and low current? It seems to contradict the relationship between current and voltage in E=IR
You are confused about the consumer load and the resistance of the cables.

The point is that power is the product of voltage and current. To transmit the same power to a consumer load, you can increase the voltage and decrease the current.

If the light in your house needs 100W, say 10A at 10V, this can be transferred from the power plant directly.

Let's say the cable between your house and the plant has 10 Ohm. If you sink 10A from the plant, the plant has to provide 110V: At 10A, a voltage drop of 100V occurs on the cable, plus the 10V you need. This means, you consume 100W while the cable wastes 1000W. 

Now, let's say your house receives 1000V.

Of course, you need a transformer to convert the delivered voltage to the voltage needed by the light!

The current consumed from the plant is now only 0.1A.

The voltage drop on the cable is now just 1V, which means 0.1W loss to power your 100W light. This is much better.

The point is the use of the transformer which allows to convert voltages and currents while maintaining the power:

$$U_1\cdot I_1=U_2\cdot I_2=const.$$