Okay, this is slightly embarassing...
I've just dug my E2 out of storage, wanting to set it up again. I've found the E2, the TTL line converter, but I've also found my very large box full of dozens of miscellaneous DC adaptors. I have no idea which one of them works with the E2. The manual doesn't say what voltage or polarity to use.
I've found an FP branded 12V positive-tip adaptor with a connector that fits --- does this sound familiar?