Ok tags or custom field filtering was important in this case. So, it seems like I can easily add the unsolved tickets that include a particular tag at the end of the month, when the report is generated, let me know if this looks like that:
I create this metric:

IF (INCLUDES_ANY([Ticket tags], "tag_name") AND [Ticket status - Unsorted] != "Closed" AND [Ticket status - Unsorted]!= "Solved")
THEN [Ticket ID]
ENDIF

And then just COUNT this metric.

We'll just have to look up the data on the report from the previous month. so if at the end of August report I need to know how many unsolved tickets we had when the month started, we'll just look at the end of July report. I was looking for a way to have that in the end of August report instead, but it's not worth the headache. Thanks!!