Hi, it's only a small thing, but E.164 format does not include the +. If it includes the plus then it is E.123 format.
The Twilio page explaining E.164 formatting is wrong.
The normal public telephone numbers we use are "International ITU-T E.164-number for geographic areas" and all E.164 numbers consist of the digit 0 to 9 only and no other characters. Spaces, symbols prefixes or suffixes do not form part of the number.
Section 12 explains that when a local code should be called in order to make an international call (e.g. dialling 00 from the UK or 011 from the USA) then E.123 suggests using the symbol + before the E.164 number. This symbol can be used when displaying the number to a human so the human can understand that they should replace the + with their local code to call internationally.
There's also a bit in section B.7 which describes CLIs and denotes that a CLI Should only be "the full international ITU-T E.164-number, i.e., country code (CC), national destination code (NDC) and subscriber number (SN). No other information, such as prefixes or symbols (e.g., "+"), should be included"