"E" to grab an object...

Slayer29179's way would be the more straightforward way to do it indeed. I suggest taking a look at Physics.Raycast to determine the object you want to pick up, and then use the raycastHit data to see if it can be picked up. If so, change its parent to be the camera and make it get dropped once the player lets go of E. Here is an example script that should be attached to the camera:

 var hit:RaycastHit;
 var pickedUpObject:GameObject;
 
 if(Input.GetKey("e")){
 if(Physics.Raycast(transform.position,transform.forward,hit,100)){//the order of the parameters might be wrong.
 if(hit.gameObject.tag=="DynamicObject"){ //i used a tag to see whether the object cn be picked up, you can use another method that may suit you better
 pickedUpObject=hit.collider.gameObject; //we use this to determine whether an object is picked up by the player. If it's not null, then the player is doing so.
 hit.gameObject.transform.parent=transform; //attach the object to the camera so it moves along with it.
 hit.gameObject.transform.position=transform.position-transform.forward; //might need changing as it's untested.
 }
 }
 }
 else if(pickedUpObject!=null){ //if player is not holding E but was picking up an object last frame
 pickedUpObject.transform.parent=null; //drop the object
 pickedUpObject=null;  //and nullify the object pointer
 }

However, the method to carry it with the camera may lead to some unwanted results such as it clipping through walls. You could either use an additional linecast to determine its position or you could poke around the DragRigidbody.js script and use its method of carrying for a more elegant solution.