Isaiah,

You may continue the path by ClickDragging from the endpoint with the Pen Tool, making sure to keep the direction of the original handle.

If that is not what you mean, you may:

1) If it is not already there, create the new path and drag the starting point to snap to the endpoint of the first path,

2) Deselect and drag over them with the Direct Selection Tool,

3) Choose which path is to govern the direction of the handles and make sure it is the topmost one in the stacking order (Layers palette/panel),

4) If needed Deselect and drag over them with the Direct Selection Tool again, Ctrl/Cmd+J to join and tick Smooth; the bottommost path will have its handle turned to align with the topmost one, without changing its length.

If that is not what you mean either, please elaborate.

Isaiah,

it is very difficult to mimic the slope of the "c", making it nearly impossible to get a smooth curve, like the "c" is just continuing on into the "e".

In the case shown, the smooth continuation of the c shape (as in closing it to become an O) would lead it very close to the e shape.

For that reason alone, it would be impossible to to start with a soft rounding from the e shape without getting inside the soft contiuation of the c shape and therby disrupting it.

You may consider using the full o shape as a template for the conitinuation of the c shape (or just use it instead for later cutting), and then extend the horizontal part of the e shape to meet it, either keeping the sharp corner or creating a simple rounding where the shapes meet.

This would leave the soft shape of the c intact and place the unavoidable transition in connexion with the e shape which has angular transitions already.

Also, as a side question, is there a way to get the slope of 1 side of the path be exactly the same as the other side?

The simple way of getting symmetry is to create one half and reflect it (with some preparation, you can do it so that the reflection is live as you draw). Depending on the shape, other ways include creating simple symmetrical shapes such as straight lines/line segments at identical angles (and joined) or ellipses, and then cutting and possibly editing Anchor Points in pairs.