You would need something like some user dropdown fields for the Assigned Engineer to be selected in. Then create a formula User field(lets call it [Current User]) and have it just be User(). Create a relationship back to your employee table using this field as the reference. Then you would compare [Current User] to the person in the assigned fields. If they match then have the form rule lets them edit the fields you want. This would only work if you had an Employee table or similar list of users in the app.
Hopefully I got that right I am just going by memory here. If not it should get you close to the goal.