Recently a new distribution, named as extended generalized exponential distribution has been introduced by Kundu and Gupta [An extension of the generalized exponential distribution, Statistical Methodology 8 (2011), pp 485-496]. In this paper we consider the extended generalized exponential distribution with known shape parameters $alpha$ and $beta$. At first, the exact expressions for the single and product moments of order statistics are derived. Then these values are used to obtain the necessary coefficients for the best linear unbiased estimators and L-moments estimators of the location and scale parameters. The mean squared errors of these estimators are also given and compared.