You sound like you are a freshman student who just walked into my Small Engines class on the first day and with a few questions thinks they can be a small engine mechanic. Craftsman is not a brand name, just a company who sells equipment they have other manufacturers build for them. E405 is not a model number, just a series name for an edger. So now you expect someone to give you a solution on how to get it running With this information. Craftsman had at least four different companies build equipment for them and at least five different engine manufacturer build engines for these companies. You did say it was a 4-cycle engine, so we can remove about 500 possible 2-cycle engines that are not on your piece of equipment. What do we have left? Too many possible combinations to even start to guess what you are dealing with. I’m asking you basic questions to narrow down what you have sitting in front of you, the same questions I ask each student in my class on the first day, so they understand that fixing a small engine is not just putting in fresh fuel and a new plug. You have to know what you are working on. Example:
Brand? LawnFlite, Poulan, Husqvarna, MTD, etc.
Model? Craftsman uses model numbers to designate which manufacturer it can from. Depending on the year it will start with a specific prefix. Check this site.
http://vintagemachinery.org/craftsman/manufacturers.aspx
Engine Brand? Clinton, Jacobson, Briggs, Tecumseh, Honda, etc.
Engine Model? Again depending on the year of manufacture, they may have numbers just like the equipment number, or use the engine manufacturer numbers.
You never answered questions 5-8, I’m assuming you understand those questions, just forgot. Most freshman get overwhelmed when they see what a mechanic needs to know before tackling a problem. Hopefully you now understand why I posted what I did.
Does your edger look like one of these? One is a Jacobson and the other is Little Wonder.