Using topology, the two features can be easily hemmed together using the Topology Edit Trace Tool and the Reshape Edge Tool, both found on the Topology Toolbar.
Note that in this example, unselected nodes are symbolized, which is found in the editing options on the Topology tab (pic). This is optional but helpful.
Your data (approximation):
Step 2. Using the Topology Edit Trace Tool, click the map window once to initial topology (and show unselected nodes).
Step 3. Click once and release on the line to be adjusted, and then move the mouse along the path that is to be adjusted.
Step 4. The path becomes pink. Click the Reshape Edge Tool.
Step 5. With the Reshape Edge Tool selected, draw the corrected path for the line. In this case, another arc is drawn along the entire arc length. Any sketch tool is possible here.
Step 6. The sketch paths are overlapping. This effectively closes that gap. There will be a line overlap that would ideally be subtracted.
Note that if there is a feature in the gap, which will be zeroed out by this process, ArcMap will return an error.