Hello @sheno for this you need to customize issue a little bit. like you have to add two date time fields such as issue raised date time and issue resolved date time. you may script so that it take values when you start and finish the issue respectively.
Now for report purpose you can do one of two things:
take a third field in issue which calculate the difference between start time and end time when you finish the issue. in this case you can make report using report builder to obtain desired report.
2.make a script report and calculate the difference between start and finish time for each issue and display it in report column.
For auto fetch of current date and time in issue raised date time you can add Now in Default textbox from customize form.
The other two you have to manage through scripting that when you close the issue it takes current date time and set in second field and set the difference in third field.