I'm not an EE, and started my foray into electronics 2 years ago... TAOE is WAY too deep for 90% of beginners simply because of the overwhelming mathematics in the text...the first 4 chapters however will get you started however before you get too intrenched into all of the mathematical-fu...at the same time I got the Mimms book...which was way too basic and left a lot to be desired in the explanation of WHY a circuit is built in a specific manner...
Really really really wish I could find some middle-ground...there are tons of excerpts on hundreds of websites for specific electronic applications, but even 'beginner kits' such as those from Adafruit and the like do not give detailed WHY's...but only how to solder the thing and perhaps make it do something nifty...