Since the inter-arrival times are independent exponentially distributed, the joint pdf of the $n$ first arrival times is
\begin{align}
f(t_1,\dots,t_n)
&=f(t_1)f(t_2|t_1)\dots f(t_n|t_{n-1})
\\&=\lambda e^{-\lambda t_1}\lambda e^{-\lambda(t_2-t_1)}\cdots \lambda e^{-\lambda(t_n-t_{n-1})}
\\&=\lambda^n e^{-\lambda t_n}
\end{align}
for $0<t_1<\dots<t_n$ and 0 elsewhere. Conditional on $n$ arrivals in $(0,T)$, the conditional pdf is
\begin{align}
f(t_1,\dots,t_n|N(T)=n)
&=\frac{f(t_1,\dots,t_n,N(T)=n)}{P(N(T)=n)}
\\&=\frac{f(t_1,\dots,t_n)P(N(T)=n|t_1,\dots,t_n)}{P(N(T)=n)}
\\&=\frac{\lambda^n e^{-\lambda t_n}e^{-\lambda(T-t_n)}}{e^{-\lambda T}(\lambda T)^n/n!}
\\&=\frac{n!}{T^n},
\end{align}
for $0<t_1<\dots<t_n<T$ and 0 elsewhere. This is the joint pdf of the order statistics of $n$ iid uniform random variables on $(0,T)$.