I too have an attention deficit and bad memory (this is why I hate interviews where you are asked to recite concepts and textbooks definitions, framework functions with parameters and so on). I get over it by understanding the concepts, understanding the big picture and researching today what I just forgot two months ago.
I think you are mistaking in believing you have trouble explaining because you use a different thought process.
For almost everyone of us, figuring a complex system means you deconstruct the system in small pieces, understand the small pieces, construct the system again in your mind along with making a kind of mind diagram about how it works. But when it comes to explain to others you use a different process than you used to figure it out. You already have that mind diagram, so you proceed like in most text books or in articles by already providing the big picture and going in details only when you feel is needed.
I also write good code, but it doesn't have anything to do with attention or memory. You write good code because you believe it's important to have something that is working well and also will be readable and maintainable. And writing good code is something almost every programmer can do if the working environments permits - i.e. they are not valuing churning bad code fast over writing good, reliable code.