Transfer time T1 to T2
With due respect to TSR2, I think that his times might be slightly on the optimistic.
On the basis that EI normally use a stand towards the end of Pier B, then allowing for a small delay at passport/immigration - yes, I know you are coming in from Dublin and therefore passports are not required but it is still technically an international arrival - you may well have used up 10 minutes before you come out into the arrivals area at T1.
Rather than going towards the information desk can I suggest that you exit via the doors to the right of WH Smith (their shop is on the left as you come out of the customs area) and then walk to the right and use the escalator that leads direct up to the Skywalk. As TSR2 says, follow the signes for The Station and then (staying on the same level) follw signs for Terminal 2 and the Radission hotel.
The Skywalk actually enters Terminal 2 at the checkin Hall level. If you are travelling with CO (??) then their checkin is usually towards the far end of the hall.
All in all I would suggest 20-25 minutes for the transfer - assuming that you are a normal fit and healthy person. Enjoy your 'flying' visit to Manchester.
Scottie Dog