You're not alone. The NV356E has a manual cord wind, not an automatic retract. The trick is in the technique, not force.
Start by guiding the plug end onto the cord hooks first. Then, use one hand to hold the vacuum steady and use your other hand to evenly loop the cord around the two cord wraps on the back. Don't just throw it on there—take an extra 10 seconds to lay each loop flat and parallel to the previous one. The last loop should secure the plug.
If it's always messy, the cord might have a 'memory' from being stored tightly coiled in the box. Straighten it out completely a few times to help it relax.
IF THAT DIDN'T WORK: Check that you're using the correct hooks. There are usually two sets: one for a shorter wrap when the cord is partly used, and one for the full-length wrap. Using the wrong hook will leave a lot of slack.
HEADS UP: A neatly wound cord isn't just about looks; it prevents the cord from getting damaged or tangled when you're moving the vacuum around.