one of the best solos on the album, i reccommend you buy HOABM if you haven't already. 
anyway, here is the solo for Hope Remains.

e-----------------------------------------------------------|
b----------------------------------------10*----------------|
g--/9--11-12-11-9--9fb-9h11p9p7-------------11-12-----------|
d-----9--9--9--9----------------------------------12fb------|
a-----------------------------------------------------------|
D-----------------------------------------------------------|

e--------------------------|
b--------------------------|
g--14hb-12-14---16hb-14-16-|
d--------------------------|
a--------------------------|
D--------------------------|

        x4                   x4
e--17-19---19---19-|--15-17---17---17-|--17fb-14-15--22fb-|
b--------15---17---|--------14---15---|-------------------|
g------------------|------------------|-------------------|
d------------------|------------------|-------------------|
a------------------|------------------|-------------------|

e--19-20-17-19-15-17-15-|-------------------------------19-19fb-20-22fb-|
b-----------------------|-------------------191919202020----------------|
g-----------------------|-151515171717191919----------------------------|
d-----------------------|-----------------------------------------------|
a-----------------------|-----------------------------------------------|
D-----------------------|-----------------------------------------------|


that's basically it, just listen for the timing.