Could anyone please tell me how to (if possible) make an electrical engine transfer energy from its own reserves to a machine, a lot faster?
You need to upgrade the Electrical Engine with a Circuit Board that has the appropriately attached Electron Tubes. To do this you will need a Carpenter to make the board, and a Thermionic Fabricator to melt the glass and other various ores to make the Electron Tubes. You will also need a soldering iron to actually attach the tubes to the circuit board.
There are several different tubes that can be added to the circuit board and each has a different effect.
Copper Electron Tubes lower the EU usage by 2, and the MJ by 1. (per tic) You can only put one Copper Tube on a board.
Bronze Electron Tubes increase the EU usage by 15, and the MJ by 4. (per tic) You can put 2 Bronze Tubes on a board.
Tin Electron Tubes increase the EU usage by 7, and the MJ by 2. (per tic) You can put 2 Tin Tubes on a board.
Iron Electron Tubes lower the EU usage by 1, and do not change the MJ output. (per tic) You can only put 1 Iron Tube on a board.
There are several Different Circuit Boards, each with a certain capaticy for tubes. More information can be found on the wiki for Electric Engines.
If what your trying to do is make the transfer of energy from the engine to the machine to be powered smoother, then your looking for Redstone Energy Cells. These are basically blocks that act as batteries for MJ. They can take inputs of up to 100MJ\t and output as much the same. These inputs and outputs are adjustable too, so you can micromanage how they move your energy around rather well.
To make these devices you will need several machines including a Magma Crucible, a Liquid Transposer, a Macerator or similar grinding machine to obtain obsidian dust, and an Induction Smelter. Although you do not need an Alloy Furnace, you will need Electrum (a mix of gold and silver) so you may want an Alloy Furnace if you dont plan on mixing dusts. You will also need some lead, some obsidian, redstone, and at least one diamond as well.
If you use the Energy Cell as a buffer between your Quarry and Engine(s) it should smooth out the energy flow between them. Keep in mind however, this would only work if there is more energy goin in than goin out, as otherwise the Quarry will pull the energy out as fast as it is being pushed in, resulting in the same effect your trying to prevent.
It's important also to note that these cells can be filled with energy, and then if a wrench is used to pick them up (shift-click) they will retain their stored energy. This allows you to fill them first and then place them to be used as a portable battery for your quarry or whatever you need.