You missed the whole point. "E=mc^2" works in metric because the units are coherent. Use the SI base units (kg, m, s) and everything works out. If you use old stuff like slugs or pound-force for mass and btu for energy, you're going to need some arbitrary conversion factor in the equation depending on which particular units you used.
The "10" business is a very small part of it; that's just to make it easier to do the math when you scale stuff. What DOES matter is that the unit of Force (for example) is exactly related to the base units: F=ma, so the base units are kg*m/s^2, and that is how you define the Newton.
In the bad old days you had to decide what units "mass" was (slugs? oz? lb? tons?) and then acceleration (ft/s? yards/s? inches/s?) and in the end you end up with some funny conversion factor depending on what you want "Force" to be in. So instead of "F=ma" you end up with "F=kma", where "F" is "poundforce", "m" is "oz", "a" is "ft/s" and "k" is some stupid conversion factor just to make the numbers work out with the units you happened to choose. And so you'll get a different conversion factor depending on which particular units you chose for mass and acceleration. Ouch.
"Slugs" are in fact the old unit of mass created to try to sort out this idiotic mess for mass, but hardly any Imperial fanatics even seem to be aware of it. In the end it was best to throw out all that garbage and realize that you only need three basic measurements: mass, distance, time. Everything else can be derived from that through physics equations. And so SI was born: "kg, m, s". Everything else is a derived unit, and so no conversion factor is EVER necessary. The multiple of 10 stuff is just to make it easy to scale numbers, and you can scale the meter down as tiny as measuring atoms to as big as measuring galaxies, but it's still just a meter with a prefix for an exponent.