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:

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

You're confusing "high voltage" with "high voltage loss". Ohm's Law governs the loss of voltage across a resistance for a given current passing through it. Since the current is low, the voltage loss is correspondingly low.

One word: Resistance. Recall that Voltage is calculated by multiplying the current by the resistance. You can have a high potential difference (which is what voltage is), and a low current, simply by having a high resistance in place to block that current.

Think of it like a water hose turned on full blast, with a hose gun attached to the end. The hose gun acts as a varying resistor controlled by the user, so even though there's high potential energy in the hose (the water wanting to flow), the resistance is so great that little to no water flows. As the user presses the trigger, the resistance lowers until water flows more and more.