Piter,

Draw a rectangle to use as a cutting object. Make the rectangle as wide as necessary to intersect at the desired places - I'm guessing where the egg should be trimmed. So if you need a longer taper, size the rectangle accordingly.

Select both your objects and Trim using the rectangle.

Select the edges around both openings and Blend.

Another possibility to make this shape in one step is to use a Rail Revolve. It would help to know what the final result should look like.

Ed Ferguson