That’s probably not the best way to think about it, so let me try again and I hope I don’t screw you up too badly;
What is it that makes a wire get hot? (consider the heating elements of many electric stoves). Those babies get glowingly hot don’t they?
Well, is not the degree to which the element heats related to the amount of current passing through it? If you want it hotter you cause more current to pass through the element, and so forth. Now, there is just about no physical thing you will likely deal with in your life that doesn’t have some inherent value of resistance to it. If you were to manipulate an experiment such that an equal amount of current were to pass through an element with a low value of resistance and then through an element with a higher value of resistance, which one do you think would feel the warmest to the touch?
It would be the element with the higher value of resistance.
I spoke about ‘manipulating the experiment’ and the reason for that was because the goal was to maintain an equal amount of current passing through the two elements. What would have actually taken place in order to maintain that identical amount of current through the two unequal resistances is that you would have had to use a higher value of voltage across the higher resistance element than you would have for the lower valued element. Now imagine that the element represented a power line which carried electricity from the local utility company to your home. Would the power company want to waste their valuable energy heating up the transmission wires when they know that nobody in their right mind would be climbing up a pole and warming their coffee there, and even if someone did there would be no meter with which to assign a dollar value to the amount of power used? So, the goal then is to get the power into your house while minimizing the amount of power wasted across the transmission lines.
It might seem counter intuitive to you at this time to see the point of increasing the voltage when as demonstrated above this led to increased heating of the element but that is only because something has been ignored. The answer to this is found by taking a look at power. Up to now we have mostly been dealing with voltage, current, and resistance… now it’s time to think about power for a moment. In the power equation you sited; P=IE, I is the current and E is the voltage. According to Ohm’s Law the voltage is also given as the product of resistance across some element multiplied by the current passing through it, that is; IR=E (don’t worry for the moment about whether an E or a V gets used in these equations, just consider them interchangeable for the time being). Watch how IR can be substituted for E in the first equation;
P=IE, but because E=IR you also have;
P=I(IR)
P=I^2R (sorry about the symbols, it should read; P equals I squared R)
So it turns out that all these critters relate to one another and the resistance of the transmission line ends up playing a role in the form of P=I^2R. But understanding that P also equals IE means that there is a way to get around the resistance of the lines while delivering the same amount of power. What took place in the experiment above was that more power was required to deliver the same current through the element with the higher resistance. The thing that ends up wasting the money is the current (I) because it produces useless heat in the wires, but because of P=IE we have a way to reduce I while maintaining the value of P… and this is done by increasing E. The voltage isn’t creating any heat and so why not raise the value of it dramatically while simultaneously reducing the amount of current and still retaining the same value of P only without all the waste.