The E-3, E-6 etc. are all based on the 707
Many of the E series were 707's, in as much they are converted ex airline aircraft, E-8C 90-0175 being ex QANTAS for example.
And if they were being pedantic, should have been C-137 variants (The E3 originally was EC-137D,) along with the C-18
The US changed the designation system in 1962, any 707 delivered after that date changed from C-137 to C-18