The battery (2M RF) can be charged in both the energizer and the EnderIO cap bank, but the Ender can only be charged in the cap bank and not the energizer.

I'm using
ActuallyAdditions-1.10.2-r93.jar
EnderIO-1.10.2-3.0.1.145_beta.jar
EnderCore-1.10.2-0.4.1.61-beta.jar

Tesla API is not present:
[09:35:00] [Client thread/TRACE] [actuallyadditions/actuallyadditions]: Sending event FMLPreInitializationEvent to mod actuallyadditions
[09:35:00] [Client thread/INFO] [Actually Additions/actuallyadditions]: Starting PreInitialization Phase...
[09:35:00] [Client thread/INFO] [Actually Additions/actuallyadditions]: Tesla not found! Skipping Tesla Power System integration.
[09:35:00] [Client thread/INFO] [Actually Additions/actuallyadditions]: Grabbing Configurations...
[09:35:00] [Client thread/INFO] [Actually Additions/actuallyadditions]: Initializing Tool Materials...
[09:35:00] [Client thread/INFO] [Actually Additions/actuallyadditions]: Initializing Armor Materials...
[09:35:01] [Client thread/INFO] [Actually Additions/actuallyadditions]: Initializing Blocks...
[09:35:01] [Client thread/INFO] [Actually Additions/actuallyadditions]: Initializing Items...
[09:35:01] [Client thread/INFO] [Actually Additions/actuallyadditions]: Initializing Fuelstuffs...
[09:35:01] [Client thread/INFO] [Actually Additions/actuallyadditions]: Initializing Update Checker...
[09:35:01] [Client thread/INFO] [Actually Additions/actuallyadditions]: PreInitializing ClientProxy...
[09:35:01] [Actually Additions Update Checker/INFO] [Actually Additions/actuallyadditions]: Starting Update Check...
[09:35:01] [Client thread/INFO] [Actually Additions/actuallyadditions]: PreInitialization Finished.
[09:35:01] [Client thread/TRACE] [actuallyadditions/actuallyadditions]: Sent event FMLPreInitializationEvent to mod actuallyadditions

In 1.10, EnderIO items pretend to still be compatible with RF when they actually don't seem to be. I can't really do anything about this, so you'll have to wait for 1.11 when Actually Additions has Forge Units compatibility and it'll definitely work. Sorry :(

EnderIO doesn't advertise RF support in 1.10 (in code, the UI still uses the RF text) - it support Forge Energy and Tesla.

I'll just add the Tesla API to my pack.