Throughout the GR lectures, we have always used (- , + , + , +) signature for the metric tensor but in some chapters it was switched to (+ , - , - , -) and immediately after that Einstein field equations were derived
$$R^{\mu \nu}- \frac{1}{2}g^{\mu \nu}R + \Lambda g^{\mu \nu} = \kappa T^{\mu \nu}$$
where $\Lambda = \frac{8 \pi G}{c^2}$. Yet without the cosmological constant, EFE in covariant form was
$$R_{\mu \nu}- \frac{1}{2}g_{\mu \nu}R = -\kappa T_{\mu \nu}$$
This part is a bit mysterious to me, because when I carry out the derivation I don't get the minus sign on the R.H.S of the equation. Additionally, according to wikipedia
$$R_{\mu \nu}- \frac{1}{2}g_{\mu \nu}R + \Lambda g_{\mu \nu} = \kappa T_{\mu \nu} \hspace{5mm} or \hspace{5mm} R_{\mu \nu}- \frac{1}{2}g_{\mu \nu}R - \Lambda g_{\mu \nu} = -\kappa T_{\mu \nu}$$
Last equation is fine since they represent EFE with different signatures. However, I wonder if there is a way to tell which signature is used in above equations.