Dan,
What you describe may be normal.
On the other hand, it may not be...
There are two things I would check - the air cleaner condition and the oil level.
First, check the air cleaner. Check that both the foam and paper elements are dry and clean. (The EH035 does not use an oiled foam element.) A dirty air filter will cause an engine to run too rich, causing soot to form on the piston and combustion chamber. An overly rich mixture will also wash the the oil film off of the cylinder walls, which causes wear leading to oil burning.
Second, make sure you have the proper amount of oil in the engine. Either too much or too little oil will cause problems. Too much oil in the crankcase will cause the engine to blow oil out the breather tube and into the intake, causing carbon build up.