Was the error that it couldn't find an explicit solution? If so, thats because when it tried so solve, it simply couldn't find any way to solve for qpl(s).
Speaking of which, I'm not sure what you are trying to do with your notation, but if you are writing L(s) meaning that L is a function of s, try writing those variables as X_s instead, which declares them as variables in the workspace which Matlab can interpret and solve for.
syms Kel Nh0 Rh fplh Nc0 Rc fplc Kgr real
syms qpl_s s
L_s = qpl(0) - Kel*qpl_s - s*qpl_s + (Nh0*Rh*fplh)/s - (Nc0*Rc*fplc)/(Kgr - s);
S = solve (L_s,qpl_s);
this gets me a solution of qpl_s as
(qpl(0) + (Nh0*Rh*fplh)/s - (Nc0*Rc*fplc)/(Kgr - s))/(Kel + s)