I am trying to explicitly solve [ if possible and if the solution exists ] a second order non-linear difference equation of the form :

$ a _ {n+2} ^2 + a_{n} ^2 + K = \lambda a_{n+1} $, where K and $\lambda$ are known positive constants ( assume K =10 and $\lambda =5 $ if you like ).

Is there any reference for it ? Or any paper that talks about the solution ?